Practice Test


Q1) Two events A and B are said to be incompatible when Show Answer


Q2) The first application of probability was done in Show Answer


Q3) Initially probability was a branch of Show Answer


Q4) Now probability is an integral part of Show Answer


Q5) The two divisions of probability are Show Answer


Q6) Subjective probability is based on Show Answer


Q7) Subjective probability is used in the field of Show Answer


Q8) An experiment is said to be Random experiment if Show Answer


Q9) The result of an experiment is called Show Answer


Q10) The two types of events are: Show Answer


Q11) The events which can be decomposed into two or more events is called: Show Answer


Q12) Two events A and B are called mutually symmetric events Show Answer


Q13) The limitation of Priori definition of probability is Show Answer


Q14) P(A) + P(A') = Show Answer


Q15) Classical definition is used in case of tossing coin, throwing dice, etc. Show Answer


Q16) Odds in favour of events are 5:4. Therefore probability of that events is Show Answer


Q17) The probability of an event is 9/16. Therefore odds against an event is Show Answer


Q18) A and A' and are mutually exclusive events Show Answer


Q19) A is called a sure event when Show Answer


Q20) A is an impossible events when Show Answer


Q21) A coin is tossed 2 times. The odds against at least 1 head is Show Answer


Q22) A - B = Show Answer


Q23) A' = Show Answer


Q24) P(A or B ) = Show Answer


Q25) P ( A or B) = ____________
when A and B are mutually Show Answer


Q26) A and B are independent events. Therefore A and B' are also independent event Show Answer


Q27) Value assigned to Random variable is from the set of: Show Answer


Q28) Number of misprints, number of tire bursting, etc. are example of: Show Answer


Q29) Height, Marks, Age are example of Show Answer


Q30) The probability of getting score 5 at least once when the die is thrown thrice Show Answer


Q31) The odds of in favour of getting a king card when a card is drawn from the pack Show Answer


Q32) When two coin are tossed simultaneously then the probability of getting atmost one head is Show Answer


Q33) For a random variable its variance is 5 then variance for (-3x +7) is Show Answer


Q34) The expected value of a random variance is always Show Answer


Q35) When 2 dice are thrown the probablility of getting the sum of the score as a perfect square is Show Answer


Q36) Two dice are thrown the probability of getting at a test are 3:7. The odds against another student passing at are 3: 5. What are the odds that both fail? Show Answer


Q37) Two dice are thrown the probability of getting at a test are 3:7. The odds against another student passing at are 3: 5. What are the odds that only the 2nd student passes? Show Answer


Q38) A salesman is known to sell a product in 3 out of 5 attempts, while another salesman in 2 out of 5 attempts. Find the probability that no sale will be affected when they both try to sell the product. Show Answer


Q39) A salesman is known to sell a product in 3 out of 5 attempts, while another salesman in 2 out of 5 attempts. Find the probability that either of them will succeed in selling the product. Show Answer


Q40) A company has production section viz. and which contribute 30%, 20% 28% and 22% respectively to the total output. It wsa observed that these sections respectively produced 1%, 2%, 3% and 4% defective units. If the units is selected at random and found to be defective, what is the probability that the unit so selected has come from either section one or section four? Show Answer


Q41) The chairman of a company needs to purchase three typewriters, each a different brand, for typing purposes. Five brands are available, which we call as A, B, C, D and E . If his selection of three typewriters is random, what is the probability that the three will include A and B,C and D or A, B and C . Show Answer


Q42) Two different digits are selected at random from digits 1, 2,........, 9. If the sum is odd, what is the probability that 2 is one of the digits selected? Show Answer


Q43) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee in which there must be one from each category. Show Answer


Q44) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee in which it should have at least one from the purchase department. Show Answer


Q45) A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase department, 2 officers of the sales department and 1 charted accountant. Find the probability of forming the committee where the chartered accountant must be in the committee. Show Answer


Q46) Two set of candidates are competing for the position on the Board of Directors of a company. The probability that first and second set will win are 0.6 and 0.4 respectively. If the first set wins, the probability of introducing a new product is 0.8 and the corresponding probability if the second set win is 0.3. What is the probability that the new product will be introduced? Show Answer


Q47) A and B choose a digit at random from 0, 1, 2,........,9 independently. Find the probability that the product of the two digits chosen is zero. Show Answer


Q48) A problem in statistics is given to two students A and B . The odds in favour of A solving the problem are 6 to 9 and against B solving the problem are 12 to 10. if A and B attempt, find the probability of the problem being solved. Show Answer


Q49) Suppose that it is 11 to 5 against a person who is now 38 years of age living till he is 73 and 5 to 3 against B now 43 living till he is 78 years. Find the chance that at least one of these persons will be alive 35 years hence. Show Answer


Q50) Two cards are drawn from a pack of 52 cards at random and kept out. Them one card is drawn from the remaining 50 cards. Find the probability that it is ace. Show Answer


Q51) A committee of 4 persons is to be appointed from 7 men and 3 women, what is the probability that the committee contains exactly two women. Show Answer


Q52) A person is known to hit a target in 5 out of 8 shots, whereas another person is known to hit it in 3 out of 5 shots. Find the probability that the target is not hit at all when they both try. Show Answer


Q53) A person throws an unbiased die. If the number shown is even, he gains an amount equal to the number shown. If the number is odd, he loses an amount equal to the number shown, find his expectation. Show Answer


Q54) A service station manager sells gas at an average of $100 per day on a rainy day, $150 on a 'dubious day', $250 on a fair day, and $300 on a clear day. If weather bureau Statistics show the probabilities of weather as follows, find his mathematical expectation:
Clear 0.50
Fair 0.30
Dubious 0.15
Rainy 0.05
Show Answer


Q55) A die tossed twice. If it shows the same number twice, Gopal gets Rs.100 otherwise he loses Rs.5. What is his mathematical expectation? Show Answer


Q56) A player tosses three fair coins. He wins Rs.8 if 3 heads occur, Rs.3 if 2 heads occur and Re.1 if only 1 head occurs. If the game is to fair, how much would he lose if no heads occur? Show Answer


Q57) In a business venture, a man can make a profit of Rs.2000 with a probability of 0.4 or have a loss of Rs.1000 with a probability of 0.6. What is his expected profit? Show Answer


Q58) A person tosses two coins simultaneously. He receives Rs.8 for two heads, Rs.2 for one head and he is to pay Rs.6 for no head. Find his expectation. Show Answer


Q59) A man draws 2 balls from a bag containing 3 white and 5 black balls. If he is to receive Rs.14 for every white ball and Rs.7 fore every black ball drawn, what is his expectation? Show Answer


Q60) 5000 tickets are sold in a lottery in which there is a first prize of Rs.10000, two second prizes of Rs.2000 each and 10 third prizes of Rs.200 each. One ticket cost Rs.2. find the expected net gain or loss if you buy one ticket? Show Answer


Q61) A player tosses 3 coins. He wins Rs.20 if all the three coins show head, Rs.10 if 2 coins show heads and Rs.5 if one head appears. If no head appears, he loses Rs.4. find his expectation. Show Answer


Q62) The probability that there is at least one error in an accounts statement prepared by A is 0.2 and for B and C , they are 0.25 and 0.4 respectively. A and B ,C prepared 10, 16 and 20 statements respectively. Find the expected number of correct statements in all. Show Answer


Q63) The probability that a man fishing at a particular place will catch 1, 2, 3, 4 fish are 0.1, 0.3, 0.2 and 0.4 respectively. What is the expected number of fish caught? Show Answer


Q64) A petrol pump proprietor sells an average of Rs.80000 petrol on rainy days and an average of Rs.95000 on clear days. Statistics from the Metereological Department show that the probability is 0.76 for clear weather and 0.24 for rainy weather on coming Monday. Find the expected value of petrol sale. Show Answer


Q65) A wheel of fortune art an amusement park is divided into five colours: red, blue, green, yellow, brown. The probabilities of the spinner landing in any of these colours are 3/10, 3/10, 2/10, 1/10, 1/10 respectively. A player can win Rs.5 if it stops on red, Rs.3 if it stops on blue, Rs.4 if it stops on green and lose Rs.2 if it stops on yellow and Re.1 if it stops on brown. Meena wants to try her luck. What is her mathematical expectation? Show Answer


Q66) If the probability that a man wins a prize of Rs.10 is 3/5 and the probablilty that he wins nothing is 2/5, find the mathematical expectation? Show Answer


Q67) Calculate the expected value of , the sum of the score when two dice are rolled. Show Answer


Q68) An investment consultant predicts that the odds against the price of a certain stock going up are 2 : 1 and the odds in favour of the price remaining the same are 1 : 3. what is the probability that the price of the stock will go down? Show Answer


Q69) What is the probability that a leap year selected at random will contain either 53 thusrdays or 53 Fridays? Show Answer


Q70) From a well shuffled pack of 52 cards, two are drawn at random. What are the odds against they being a king and an ace? Show Answer


Q71) A chartered accountant applies for a job in two firms X and Y , he estimates that the probability of his being selected in firm X is 0.7 and being selected at Y is 0.5 and the probability of at least one of is applications being rejected is 0.6. What is the probability that he will be selected in one of the firms? Show Answer


Q72) There are 4 letters and 4 addressed envelopes. Find the chance that all letters are not dispatched in the right envelopes. Show Answer


Q73) A certain player X is known to win with probability 0.3 if the track is fast and 0.4 if the track is slow. For Monday, there is a 0.7 probability of a fast track and 0.3 probability of a slow track. What is the probability that the player X will win on Monday? Show Answer


Q74) A pair of dice is thrown and sum of the numbers on the two dice is observed to be 6. what is the probability that there is 2 on one of the dice? Show Answer


Q75) A die is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. What is the probability that sum of the two numbers shown is even? Show Answer


Q76) An urn contains 10 counters on which digits 0, 1, 2, ......9 are written one digit on each counter, no digit being repeated. A chooses a counter first and then B chooses another counter ( the first is not replaced). Find the probability that the product of the two digits chosen in zero. Show Answer


Q77) There are four hotels in a certain town. If 3 men check into hotels in a day, what is the probability that each check into a different hotels? Show Answer


Q78) Two different digits are selected at a random from the digits 1,2,......9. If the sum is odd what is the probability that 2 is one of the digits selected? Show Answer


Q79) It is known that 40% of the students in a certain college are girls and 50% of the students are above the median height. If 2/3 of the boys are above the median height, what is the probability that a randomly selected student who is below the median height is a girl? Show Answer


Q80) Four digits 1, 2, 4 and 6 are selected at random to form a four digit number. What is the probability that the number so formed, would be divisible by 4? (Repetition is allowed) Show Answer


Q81) Anita and Binita stand in a line with 7 other people. What is the probability that there are 4 persons between them? Show Answer


Q82) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed at least in one of the subjects. Show Answer


Q83) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed none of the above subjects Show Answer


Q84) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed only in Maths. Show Answer


Q85) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed only in Statistics. Show Answer


Q86) Out of 80 students in a class, 30 passed in Mathematics, 20 passed in Statistics and 10 passed in both. One student is selected at random. Find the probability that he has passed exactly in one of the subjects. Show Answer


Q87) If x is a continuous random variable over the interval [a, b] then for f (x) to be a probability density function the conditiond are Show Answer


Q88) E(x and y) =E(x). E(y) provided Show Answer


Q89) The value E(10) is Show Answer


Q90) P(A-B) = Show Answer


Q91) P(A) = P(B) =5/9, P(A-B)=2/9 Show Answer


Q92) If x and y are 2 random variable having expected value 7 and 5 respectively the expected value of E(x+y) Show Answer


Q93) If x and y are 2 random variable such that y =8 -7x then v(y) is given by Show Answer


Q94) Initially, probability was a branch of Show Answer


Q95) Two broad divisions of probability are Show Answer


Q96) Subjective probability may be used in Show Answer


Q97) An experiment is known to be random if the results of the experiment Show Answer


Q98) The classical definition of probability is based on the feasibility at subdividing the possible outcomes of the experiments into Show Answer


Q99) An event that can be split into further events is known as Show Answer


Q100) If events are mutually exclusive, then Show Answer


Q101) Which of the following pairs of events are mutually exclusive? Show Answer


Q102) If two events A and B are independent, then Show Answer


Q103) If two events A and B are independent, then Show Answer


Q104) The complete group of all possible outcomes of a random experiment given set of events. Show Answer


Q105) When none of the outcomes is favourable to the event then the event is said to be Show Answer


Q106) If one of outcomes cannot be expected to occur in preference to the other in an experiment the events are Show Answer


Q107) If P(A) = 1, then the event A is known as Show Answer


Q108) If an unbiased coin is tossed once, then the two events head and tail are Show Answer


Q109) The probability of an event can assume any value between Show Answer


Q110) _____ of all probabilities is equal to 1. Show Answer


Q111) Sum of probability of an event A and its complement is Show Answer


Q112) Probability of occurrence of atleast one of the events A and B is denoted by Show Answer


Q113) Probability of occurrence of A as well as B is denoted by Show Answer


Q114) If A, B and C are mutually exclusive independent and exhaustive events then what is the probability that they occur simultaneously? Show Answer


Q115) When the no. of cases favourable to the event A=0 then P(A) is equal to Show Answer


Q116) For two events A and B, P(B) = 0.3, P(A but not B) = 0.4 and P(not A) = 0.6. The events A and B are Show Answer


Q117) If P (A) = 5 / 11 then probability of complement of A is equal to Show Answer


Q118) If A and B are mutually exclusive events and P(A) = 0.3 and P(B) = 0.4, find P(A') Show Answer


Q119) All possible outcomes of a random experiment forms the Show Answer


Q120) S = {1, 2, 3, 4, 5, 6} is the _____ when a die is tossed. Show Answer


Q121) The value of P(S) were S is the sample space is Show Answer


Q122) The probability space in tossing two coins is Show Answer


Q123) Which set of function define a probability space on S {A, B, C}? Show Answer


Q124) Which of the following set of function define a probability space on S={A, B, C} Show Answer


Q125) Let P be a probability function on S = {X1, X2, X3} if P(X1) = 1/4 and P(X3) = 1/3 then P(X2) is equal to Show Answer


Q126) The probability of occurrence of atleast one of the 2 events A and B (which may not be mutually exclusive) is given by Show Answer


Q127) If P(A -B) = P(B - A), then the two events A and B satisfy the condition Show Answer


Q128) For any two events A and B Show Answer


Q129) For any two events A and B Show Answer


Q130) Three events A, B, and C are mutually exclusive, exhaustive and equally likely. What is the probability of complementary event of A? Show Answer


Q131) If P(A)=1/5, P(B)=1/2 and A and B are mutually exclusive then P(AB) is Show Answer


Q132) A, B and C are three mutually exclusive and exhaustive events such that P(A) = 2 P(B) = 3 P(C). What is P(B)? Show Answer


Q133) According to the statistical definition of probability, the probability of an event A is the Show Answer


Q134) If A, B and C are mutually exclusive and exhaustive events, then P(A) + P(B) + P(C) equals to Show Answer


Q135) If P(A) = 6/9 then the odds against the event is Show Answer


Q136) If p:q are the odds in favour of an event, then the probability of that event is Show Answer


Q137) The odds in favour of one student passing a test are 3:7. The odds against another student passing at are 3:5. The probability that both pass is Show Answer


Q138) The odds in favour of one student passing a test are 3:7. The odds against another student passing at are 3:5. The probability that both fail is Show Answer


Q139) The odds in favour of an event is 2:3 and odds against another event is 3:7. Find the probability that only one of the two events occurs. Show Answer


Q140) A bag contains 20 discs numbered 1 to 20. A disc is drawn from the bag. The probability that the number on it is a multiple of 3 is Show Answer


Q141) Find the probability that a four digit number comprising the digits 2, 5, 6 and 7 would be divisible by 4. Show Answer


Q142) A number is selected from the set S = {1, 2, 3, 4 ..... 25}. The probability, that it would be divisible by 4 or 7, is Show Answer


Q143) A bag contains 30 balls numbered from 1 to 30. One ball is drawn at random. The probability that the number of the drawn ball will be multiple of 3 or 7 is Show Answer


Q144) A bag contains 6 green and 5 red balls. One ball is drawn at random. The probability of getting a red ball is? Show Answer


Q145) Out of numbers 1 to 120, one is related at random what is the probability that it is divisible by 8 or 10. Show Answer


Q146) There are 10 balls numbered from 1 to 10 in a box. If one of them is selected at random, what is the probability that the number printed on the ball would be an odd number greater that 4? Show Answer


Q147) If the letters of the word ATTEMPT are written down at random, the chance that all Ts are consecutive is Show Answer


Q148) If two letters are taken at random from the word HOME, what is the probability that none of the letters would be vowels? Show Answer


Q149) If a coin is tossed twice, then the events 'occurrence of one head', 'occurrence of 2 heads' and 'occurrence of no head' are Show Answer


Q150) If an unbiased coin is tossed twice, the probability of obtaining at least one tail is Show Answer


Q151) A coin is tossed two times. The toss resulted in one head and one tail. What is the probability that the first throw resulted in tail? Show Answer


Q152) Two unbiased coins are tossed. The probability of obtaining one head and one tail is Show Answer


Q153) Two unbiased coins are tossed. The probability of obtaining atleast one head is Show Answer


Q154) When two unbiased coins are tossed, the probability of getting both heads or both tails is Show Answer


Q155) When 3 unbiased coins are tossed. The probability of obtaining not less than 3 heads is Show Answer


Q156) Three coins are tossed together. The probability of getting exactly two heads is Show Answer


Q157) The probability that atleast one head appears in a single throw of three fair coins is Show Answer


Q158) 4 coins are tossed. The probability that there are 2 heads is Show Answer


Q159) Probability of throwing an even number with an ordinary six faced die is Show Answer


Q160) The probability of throwing more than 5 in a single throw from an ordinary die is Show Answer


Q161) If two unbiased dice are rolled, what is the probability of getting points neither 6 nor 9? Show Answer


Q162) If two unbiased dice are rolled together, what is the probability of getting no difference of points? Show Answer


Q163) Two dice are thrown together. The probability that 'the event the difference of nos shown is 2 is Show Answer


Q164) Two dice are thrown together. The probability of the event that the sum of nos. shown is greater than 5 is Show Answer


Q165) In a single throw with two dice the probability of getting a sum of five on the two dice is Show Answer


Q166) What is the chance of throwing atleast 7 in a single cast with 2 dice? Show Answer


Q167) The chance of getting a sum of 10 in a single throw with two dice is Show Answer


Q168) Two dice with face marked 1, 2, 3, 4, 5, 6 are thrown simultaneously and the points on the dice are multiplied together. The probability that product is 12 is Show Answer


Q169) A card is drawn from a well-shuffled pack of playing cards. The probability that it is a spade is Show Answer


Q170) A card is drawn from a well-shuffled pack of playing cards. The probability that it is a king is Show Answer


Q171) The probability that a card drawn at random from the pack of playing cards may be either a queen or an ace is Show Answer


Q172) A card is drawn from a pack of 52 cards. What is the probability that it is neither a black card nor a king? Show Answer


Q173) What is the chance of picking a heart or a queen not of heart from a pack of 52 cards? Show Answer


Q174) Two cards are drawn from a well shuffled pack of playing cards. Find the probability that both are ace. Show Answer


Q175) Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that they are both kings if the first is replaced. Show Answer


Q176) A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of getting two kings? Show Answer


Q177) A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of getting two hearts? Show Answer


Q178) If probability of drawing a spade from a well- shuffled pack of playing cards is 1/4 then the probability that of the card drawn from a well- shuffled pack of playing cards is 'not a spade' is Show Answer


Q179) A card is drawn from each of two well-shuffled packs of cards. The probability that atleast one of them is an ace is Show Answer


Q180) If a card is drawn at random form a pack of 52 cards, what is the chance of getting a Spade or an ace? Show Answer


Q181) The probability of drawing a black ball from a bag containing 8 white and 5 black balls Show Answer


Q182) A bag contains 10 red and 10 green balls. A ball is drawn from it. The probability that it will be green is Show Answer


Q183) A bag contains 5 red and 3 yellow balls. Two balls are drawn at random one after the other without replacement. The probability that both balls drawn are yellow is Show Answer


Q184) A bag contains 3 red, 6 white, and 7 blue balls. If two balls are drawn at random, then the probability of getting both white balls is Show Answer


Q185) A box contains 6 red, 7 white and 4 blue balls. The number of ways in which the selection of three balls can be made so that none is red is Show Answer


Q186) There are two boxes containing 5 white and 6 blue balls and 3 white and 7 blue balls respectively. If one of the boxes is selected at random and a ball is drawn from it, then the probability that the ball is blue is Show Answer


Q187) A bag contains 2 Red, 3 Green, and 2 Blue balls. If 2 balls are drawn at random from the bag find the Probability that none of them will be Blue. Show Answer


Q188) A box contains 5 white and 7 black balls. Two successive draws of 3 balls are made (i) with replacement (ii) without replacement. The probability that the first draw would produce white balls and the second draw would produce black balls are respectively Show Answer


Q189) 8 identical balls are placed at random in three bags. What is the probability that the first bag will contain 3 balls? Show Answer


Q190) There are two urns containing 5 red and 6 white balls and 3 red and 7 white balls respectively. If two balls are drawn from the first urn without replacement and transferred to the second urn and then a draw of another two balls is made from it, what is the probability that both the balls are red? Show Answer


Q191) If one ball is drawn at random from each of that three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls then the probability that 2 white and 1 black balls will be drawn, is Show Answer


Q192) There are two urns. The first urn contains 3 red and 5 white balls whereas second contains 4 red and 6 white balls. A ball is taken at random from the first urn and is transferred to the second urn. Now another ball is selected at random from the second urn. The probability that the second ball would be red is Show Answer


Q193) A bag contains 8 red and 5 white balls. Two successive draws of 3 balls are made without replacement. The probability that the first draw will produce 3 white balls and the second 3 red balls is Show Answer


Q194) There are three boxes with the following composition:
Box I: 5 Red + 7 White + 6 Blue balls;
Box II: 4 Red + 8 White + 6 Blue balls;
Box III: 3 Red + 4 White + 2 Blue balls
If one ball is drawn at random, then what is the probability that they would be of same colour? Show Answer


Q195) A packet of 10 electronic components is known to include 2 defectives. If a sample of 4 components is selected at random from the packet, what is the probability that the sample does not contain more than 1 defective? Show Answer


Q196) What is the chance of getting atleast one defective item if 3 items are drawn randomly from a lot containing 6 items of which 2 are defective item? Show Answer


Q197) The independent probabilities that the three sections of a costing department will encounter a computer error are 0.2, 0.3 and 0.1 per week respectively. What is the probability that there would be one and only one computer error per week? Show Answer


Q198) The independent probabilities that the three sections of a costing department will encounter a computer error are 0.2, 0.3 and 0.1 per week respectively. What is the probability that there would be at least one computer error per week? Show Answer


Q199) It is given that a family of 2 children has a girl, what is the probability that the other child is also a girl? Show Answer


Q200) A class consists of 10 boys and 20 girls of which half the boys and half the girls have blue eyes. Find the probability that a student chosen random is a boy and has blue eyes Show Answer


Q201) Mr. Roy is selected for three separate posts. For the first post, there are three candidates, for the second, there are five candidates and for the third, there are 10 candidates. What is the probability that Mr. Roy would be selected? Show Answer


Q202) Following are the wages of 8 workers in rupees: 50, 62, 40, 70, 45, 56, 32, 45: If one of the workers is selected at random, what is the probability that his wage would be lower than the average wage? Show Answer


Q203) A committee of 7 members is to be formed from a group comprising of 8 gentlemen and 7 ladies. What is the probability that the committee would comprise of at least 2 ladies? Show Answer


Q204) There are 7 seats in a row. Three persons take seats at random. The Probability that the middle seat is always occupied and no two persons are consecutive is Show Answer


Q205) The probability that A speaks truth is 4/5, while the probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact is Show Answer


Q206) A problem in probability was given to three CA students A, B and C whose chances of solving it are 1/3, 1/5 and 1/2 respectively. What is the probability that the problem would be solved? Show Answer


Q207) If the overall percentage of success in an exam is 60, what is the probability that out of a group of 4 students, at least one has passed? Show Answer


Q208) If the probability of a horse A winning a race is 1/6 and the probability of a horse B winning the same race is 1/4, what is the probability that one of the horses will win Show Answer


Q209) An experiment succeeds twice as often as it fails. What is the probability that in next five trials there will be three success. Show Answer


Q210) If on an average 9 ships out of 10 return safely to a port. The probabilities that a ship returns safely is Show Answer


Q211) A man can kill a bird once in five shots. The probabilities that a bird is not killed is Show Answer


Q212) Rupesh is known to hit a target in 5 out of 9 shots whereas David is known to hit the same target in 6 out of 11 shots. What is the probability that the target would be hit once they both try? Show Answer


Q213) There are three persons A, B and C having different .ages. The probability that A survives for another 5 years is 0.80, B survives for another 5 years is 0.6C and C survives for another 5 years is 0.50. The probabilities that A and B survive for another 5 years is 0.46, B and C survive for another 5 years is 0.32, A and C survive for another 5 years is 0.48 and probability that all will survive is 0.26. Find the probability that at least one of them survives for another 5 years. Show Answer


Q214) What is the probability that a leap year selected at random would contain 53 Saturdays? Show Answer


Q215) What is the probability that 4 children selected at random would have different birthdays? Show Answer


Q216) There are 6 positive and 8 negative numbers. Four numbers are selected at random without replacement and multiplied. Find the probability that the product is positive: Show Answer


Q217) Baye's Theorem is useful in Show Answer


Q218) The conditional probability of an event B on the assumption that another event A has actually occurred is given by Show Answer


Q219) If P(A/B) = P(A), then Show Answer


Q220) P(B/A) is defined only when Show Answer


Q221) In formula P(B/A), P(A) is Show Answer


Q222) P(A/B') is defined only when Show Answer


Q223) The Theorem of Compound Probability states that for any two events A and B. Show Answer


Q224) Given P(A) = 1/2, P(B) = 1/3, P(AB) = 1/4, the value of P(A/B) is Show Answer


Q225) A and B are two events such that P(A)=1/3, P(B)=1/4, P(A+B)=1/2, then P(B/A) is equal to Show Answer


Q226) If the outcome is an odd number when a dice is rolled, then the probability that it is a prime number is Show Answer


Q227) A pair of dice is rolled. If the sum on the dice is 9, find the probability that one of dice showed 3. Show Answer


Q228) A pair of dice is thrown and sum of the numbers on the two dice comes to be 7. What is the probability that the number 3 has come on one of the dice? Show Answer


Q229) A pair of dice is thrown together and the sum of points of the two dice is noted to be 10. What is the probability that one of the two dice has shown the point 4? Show Answer


Q230) A family has 2 children. The probability that both of them are boys if it is known that one of them is a boy Show Answer


Q231) The probability of the occurrence of a no. greater than 2 in a throw of a dice if its is known that only even nos. can occur is Show Answer


Q232) A player has 7 cards in hand of which 5 are red and of these five, 2 are kings. A card is drawn at random. The probability that it is a king, it being known that it is red is Show Answer


Q233) In a class 40% students read Maths, 25% Biology and 15% both Maths and Biology. One student is selected at random. The probability that he reads Maths if it is known that he read Biology is Show Answer


Q234) Value of a random variable are Show Answer


Q235) Expected value of a random variable Show Answer


Q236) If all the values taken by a random variable are equal then Show Answer


Q237) If x and y are independent, then Show Answer


Q238) Mean is the Expected Value of x for a Show Answer


Q239) Variance of a random variable x is given by Show Answer


Q240) f (x), the probability mass function of a random variable x satisfies Show Answer


Q241) Which of the following is the characteristic of the probability distribution of a random variable? Show Answer


Q242) Probability mass function is always Show Answer


Q243) The sum of probability mass function is equal to Show Answer


Q244) When X is a continuous function f(x) is called Show Answer


Q245) If If x and y are random variables having expected values as 4.5 and 2.5 respectively, then the expected value of (x-y) is Show Answer


Q246) If a random variable x assumes the values 0, 1 and 2 with probabilities 0.30, 0.50 and 0.20, then its expected value is Show Answer


Q247) The expected value of X, the sum of the scores, when two dice are rolled is Show Answer


Q248) A packet of 10 electronic components is known to include 3 defectives. If 4 components are selected from the packet at random, what is the expected value of the number of defective? Show Answer


Q249) The probability that there is atleast one error in an account statement prepared by 3 persons A, B and C are 0.2, 0.3 and 0.1. If A, B and C prepare 60, 70 and 90 such statements, then the expected number of correct statements Show Answer


Q250) A bag contains 6 white and 4 red balls. If a person draws 2 balls and receives Rs. 10 and Rs. 20 for a white and red ball respectively, then his expected amount is Show Answer


Q251) In a business venture, a man can make a profit of Rs. 50000 or incur a loss of Rs. 20000. The probabilities of making profit or incurring loss, from the past experience, are known to be 0.75 and 0.25 respectively. What is his expected profit? Show Answer


Q252) A box contains 12 electric lamps of which 5 are defectives. A man selects three lamps at random. What is the expected number of defective lamps in his selection? Show Answer


Q253) Moidul draws 2 balls from a bag containing 3 white and 5 red balls. He gets Rs. 500 if he draws a white ball and Rs. 200 if he draws a red ball. What is his expectation, if he is asked to pay Rs. 400 for participating in the game, would he consider it a fair game and participate? Show Answer


Q254) A number is selected at random from a set containing the first 100 natural numbers and another number is selected at random from another set containing the first 200 natural numbers. What is the expected value of the product? Show Answer


Q255) A random variable X takes values. 0, 1, 2, 3, and its mean is 1.3. If P(X = 3) = 3P(X = 1), and P(X = 2) = 0.3, then P(X = 0) is Show Answer


Q256) X is a discrete random variable which takes The value 0, 1, 2 and P(X = 0) = 144 / 169 P (X = 1) = 1/169 Then the value of P (X = 2) is Show Answer


Q257) An unbiased coin is tossed three times. Find the expected value of number of heads and also its standard deviation. Show Answer


Q258) The expected no. of head in 100 tosses of an unbiased coin is Show Answer


Q259) If the probability of a defective bolt is 0.1, find the standard deviation for the distribution of defective bolt in a total of 500. Show Answer


Q260) A dice is rolled thrice, if getting a four is considered a success, find the variance of probability distribution of number of success. Show Answer


Q261) If a variance of a random variable x is 23, then what is the variance of 2 x + 10? Show Answer


Q262) A Player tosses 3 coins. He wins Rs. 5 if 3 heads appear, Rs. 3 if two heads appear, Rs. 1 if one head appear. Find his expected Gain in Rs. _____. Show Answer


Q263) In a class of 80 students, 35% play only cricket, 45% only Tennis, How many play Cricket? Show Answer


Q264) A question paper consist 10 questions, 6 in math and 4 in stats. Find out number of ways to solve question paper if at least one question is to be attempted from each section. Show Answer


Q265) There are 6 gents and 4 ladies. A committee of 5 is to be formed if it include at least two ladies. Show Answer


Q266) When an unbiased dice is rolled, find the odds in favour of getting of multiple of 3. Show Answer


Q267) Three coins are rolled , what is the probability of getting exactly two heads: Show Answer


Q268) If a random sample of 500 Oranges Produces 25 rotten oranges. Than the estimate of the proportion of rotten oranges in the sample is: Show Answer


Q269) Two letter are drawn at random from word "HOME" find the probability that there is no vowel. Show Answer


Q270) A bag contains 15 one rupee coins, 25 two rupee coins and 10 five rupee coins. If a coin is selected at random from the bag, then the probability of not selecting a one rupee coin is: Show Answer


Q271) The sum of two numbers obtained in a single throw of two dice is 'S'. Then the probability of 'S' will be maximum when 'S'= Show Answer


Q272) An unbiased coin is tossed 3 times, the expected value of the number of heads is: Show Answer


Q273) If 6 coins are tossed simultaneously then the probability of obtaining exactly 2 heads is Show Answer


Q274) A die is thrown twice then the probability that the sum of the numbers is divisible by 4 is Show Answer


Q275) Two event A and B are such that they do not occurs simultaneously then they are called______events. Show Answer


Q276) If a coin is tossed 5 times then the probability of getting Tail and Head occurs alternatively is Show Answer


Q277) When 2 dice re thrown simultaneously then the probability of getting at least one 5 is Show Answer


Q278) Two letters are choosen from the word HOME. What is the probability that the letters choosen are not vowels. Show Answer


Q279) If A,B,C are three mutually exclusive and exhaustive events such that: p(A) =2(B)= 3P (C) what is P(B)? Show Answer


Q280) What is the probability of getting 7 or 11 when two dices are thrown? Show Answer


Q281) A log contains 15 one rupee coins, 25 two rupees coins and 10 five rupee coins if a coin is selected t random than probability for not selecting a one rupee coin is: Show Answer


Q282) When 2fair dice are thrown what is the probability of getting the sum which is a multiple of 3? Show Answer


Q283) When 2 coins are tossed simultaneously the probability of getting at least one tail? Show Answer


Q284) When 3 dice are rolled simultaneously the probability of a number on the third die is greater than the sum of the numbers on two dice. Show Answer


Q285) If a space 75% of truth and B speaks 80% of truth. In what percentage both of them likely contradict with each other in narrating the same questions? Show Answer


Q286) An event that can be subdivided into further events is called as. Show Answer


Q287) Three identical and balanced dice are rolled. The probability that the same number will appear on each of them is. Show Answer


Q288) A basket contains 15 white balls, 25 red balls and 10 blue balls. If a ball is selected at random, the probability of selecting not a white ball. Show Answer


Q289) 2 dice are thrown simultaneously. The probability of a total score of 5 from the out comes of dice is. Show Answer


Q290) If an unbaised coin is tossed twice, then the probability of obtaining at least one tail is. Show Answer


Q291) If an unbiased coin is tossed three times, what is the probability of getting more than one head? Show Answer


Q292) If there are 48 marbles market with numbers 1 to 48, then the probability of selecting a marble having the number divisible by 4 is: Show Answer


Q293) A bag contains 7 blue and 5 green balls. One ball is drawn at random. The probability of getting a blue ball is_______. Show Answer


Q294) The probability that a football team loosing a match at Kolkata is 3/5 and winning a match at Bengaluru is 6/7; the probability of the team winning at least one match is___________. Show Answer


Q295) If in class, 60% of the student study, Mathematics and science and 90% of the student study science, then the probability of a student studying mathematics given that he/she is already studying science is: Show Answer


Q296) If there are 16 phones, 10 of them are Android and 6 of them are of Apple, then the probability of 4 randomly selected phones to include 2 Android and 2 Apple phone is: Show Answer


Q297) A biased coin is such that the probability of getting a head is thrice the probability of getting a tail, if the coin is tossed 4 times, what is the probability of getting a head all the time? Show Answer


Q298) Which of the following pair of events E and F are mutually exclusive? Show Answer


Q299) Assume that the probability for rain on a day is 0.4. An umbrella salesman can rain Rs 400 per day in case of rain on that day and will lose Rs100 per day if there is no rain. The expected earnings in per day of the salesman is Show Answer


Q300) In a group of 20 males and 15 females, 12 males and 8 females are service holders. What is the probability that a person selected at random from the group is a service holder given that the selected person is a male? Show Answer


Q301) There are 3 boxes with the following composition:
Box I: 7Red+5White+4Blue balls,
Box II: 5Red+6White+3Blue balls,
Box III: 4Red+3White+2Blue balls. One of the boxes is selected at random and a ball is drawn from it. What is the probability the drawn ball is red? Show Answer


Q302) A dice is rolled twice. Find the probability of getting numbers multiple of 3 or 5? Show Answer


Q303) what is the probability of occurrence of leap year having 53 Sunday ? Show Answer


Q304) If in a bag of 30 balls numbered from 1 to 30. Two balls are drawn find probability of getting a ball being multiple of 2 or 5 Show Answer


Q305) Two perfect dice are rolled what is the probability that one appears at least in one of the dice? Show Answer


Q306) If two dice are rolled an done of the dice shows 1 at a point then how many such outcome can be done where it is known that its probability is x/36, where x= __________.
Show Answer


Q307) If P,Q are the odds in favour of an event, then the probability of that event is- Show Answer


Q308) A machine is made of two part A and B.The manufacturing process of each part is such that probability of defective in part A is 0.08 and that B is 0.05.What is the probability that the assembled part will not have any defect?
Show Answer


Q309) The probability that a leap year has 53 Monday is :
Show Answer


Q310) The Theorem of Compound Probability states that for any two events A and B.
Show Answer


Q311) If a number is selected at random from he first 50 natural numbers, what will be the probability that the selected number is a multiple of 3 and 4?
Show Answer


Q312) If three coins are tossed simultaneously,what is the probability of getting two heads together? Show Answer


Q313) Four persons are chosen at random frame a group of 3 men, 2 women and 4 children. The probability that exactly 2 of then are children is? Show Answer


Q314) If P(A)=1/3, P(B)=1/4, P(A/B)=1/6, the probability P(B/A) is Show Answer


Q315) Company A produces 10% defective products, company B produces 20% defective products, company C produces 5% defective products.If choosing company is an equally likely events.What is probability that the product.Chosen is free from defect.
Show Answer


Q316) For any two events A and B.It is P(A)=2/3, P(B)=3/8 and P(A/B)=1/4.Then the events A and B are Show Answer


Q317) The Probability that a 4-digit number comprising the digit 2, 5, 6 and 7 without reflection of digits would be divisible by 4.
Show Answer


Q318) On a commodity exchange when booking traits with provision for stop strider can make a profit of Rs 50,000 or incur a loss of Rs 20,000.The probability of making profit an incurring losses from the part experience are known to be ___________and 0.5 respectively.The expected profit to be made by trader should be.
Show Answer


Q319) A box contain 20 electrical bulb out of which 4 are defective.Two bulbs are chosen at random from this box.The probability that at least one of them is defective. Show Answer


Q320) If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Club or a King?
Show Answer


Q321) A number is selected from the first 30 natural numbers.What is the probability that it would be divisible by 3 or 8?

Show Answer


Q322) A number is selected at random from the first 100 natural numbers.What is the probability that it would be a multiple of 3 or 7? Show Answer