# 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

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= __________.

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?

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

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

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?

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.

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.

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.

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?