Practice Test


1) The probability that A wins a game of chess against B is 2 / 3. Find the probability that A wins at least 'one' game out of the games he plays against B.


2) If X is a poison random variable such that , p(x=3) = p(x=4), find the mean and standard deviation of the distribution.


3) A coin is tossed 4 times. Find the probability of getting exactly 3 heads.


4) In a binomial distribution, mean and variance are 12 and 4 respectively. Find the parameters of the distribution.


5) If for a poison distribution 3P (2) = P (3), Find the mean and standard deviation of the distribution.


6) Calculate mean and variance of Poisson variable X if P(X = 4) = P(X = 5).


7) Six fair coins are tossed simultaneously. Find the probability of getting exactly three heads.


8) On an average A can solve 60% of the problems. What is the probability of A solving exactly 5 problems out of 6.


9) If x a Poisson variate and if P ( X = 1) = P (X = 2), find its mean and standard deviation.


10) The random variable X defined as x = number of defective articles, follows Poisson distribution. If for a sample of 400 articles P(x=3) = 5P(X=5), find p, the probability of a defective article.


11) If for a binomial distribution, number of trials is 9, the variance is 2, and the probability of success is greater than that of failure, find the probabilities of both:
Success and Failure.


12) In a certain factory there are 25% unskilled workers. Find the probability that in a sample of 5 workers selected from this factory exactly 4 are unskilled workers.


13) When a particular coin is tossed 4 times, it was observed that head appeared on its top face 3 times. If the same coin is tossed 5 times find the probability of getting exactly 2 heads.


14) It is known that 20% of the bulbs manufactured by a company are defective. The binomial variate X is defined to be the number of defective bulbs and the total number of bulbs bought is 10. Find the mean and the variance of the distribution.


15) If for a Poisson Distribution
P(X=2) + P(X=3) = P(X=4), then find the mean of the distribution.


16) On an average, A can solve 40% of the problems. What is the probability of A solving exactly 4 problems out of 6?


17) Find n and p for the binomial distribution if mean is 6 and standard deviation is 2.


18) Six coins are tossed simultaneously. What is the probability of getting 2 heads.


19) For a binomial distribution probability of 1 and 2 success are 0.4096 and 0.2048. Find p.


20) How many tosses of a coin are needed so that the probability of getting at least on head is 87.5%.


21) On an average A can solve 40% of the problem. What is the probability if A solving exactly 4 problems out of 6.


22) An unbiased die is thrown 5 times and occurance of 1 or 6 is considered as success. Find the probability of at least one success.


23) Assuming that half of the the MBA's are commerce graduates and that the in investigators interview 10 MBA's to see whether they are commerce graduates what is the probability that 2 or less number of MBA's will be commerce graduates.


24) The overall percentage of failures in an examination is 40, what is the probability that out of a group of 6 candidates at least 4 passed the exam.


25) A fair dice rolled 5 times getting an even number is considered as success. Find the probability of no successes.


26) A commercial jet aircraft has four engines. For an aircraft to land safely, at-least two engines should be in working conditions. Each engine has an independent reliability of 92%. What is probability that an aircraft in flight can land safely?


27) The incidence of occupational disease in an industry is such that the workman has a 25% chance of suffering from it. What is the probability that out of 6 workmen, 4 or more will contact the disease ?


28) Find the probability of guessing correctly at least six of the ten answers in a TRUE or FALSE objective test.


29) It is observed that it rains on 12 days out of 30 days. Find the probability that : it rains on exactly 3 days of week.


30) The probability that a student from an evening college will be a graduate is 0.4. Determine the probability that out of 5 students none students will gradates?


31) A certain television tube has a probability of 0.3 of functioning more than 400 hours. If 15 tubes are tested, find the probability that exactly 4 of them will function more than 400 hours. What is the expected number of tubes tat will last more than 400 hours.


32) The probability of failure in Economics paper is 20%. If 25 batches of 6 students appear for the examination, in how many batches 4 or more students will pass?


33) A doctor from his past experience that 10% of the patients to whom he prescribes certain drug will have undesirable side effects. Find the probability that among 12 patients to whom he prescribes drug atmost 2 will will have undesirable side effects.


34) A lot of 100 pens contains 10 defective pens. 5 pens are selected at random from the lot and sent to the retail store, what is the probability that the store will receive at least one defective pen?


35) If p=0.42, then the probability of 2 successes in trials is


36) A factory produces bulbs. the probability that a bulb will fuse after 200 hours of use is 0.02. find the probability that not more then 1 out of 4 bulbs fuse after 200 hours of uses


37) Describe a trial (n) and a success (x) and find the probability for success (p) for the problem:21% of the bolts produced by machine are defective. Out of 6 bolts chosen at random, what is the probability that 2 are defective ?


38) From the past experience, 2 out of 3 patient admitted to the hospital are cured . If 6 patient are admitted, then the probability of 4 patient being cured is


39) A machine is known produce 10% defective item. Then the probability that log of 10 items produced by the machine does not contain defective item is


40) In a binomial distribution with n=4, if 2P(X=3)=3P(X=2), then value of p is


41) The total area under the standards normal curve is


42) If the mean of the binomial distribution is 25 then S.D. lies in the interval


43) Standard normal variable z has the following p.d.f


44) The mean and variance of a binomial distribution are 6 and 4 . The parameter n is


45) The number of times a fair coin is tossed that the probability of getting at least one head is at least 0.95


46) Number of stars in the sky is an example of


47) In a meeting 70% of member favour a certain proposal, 30% being in position. A member is selected at random and let X = 0 if he opposes the proposal, and X=1 if he is in favour of the proposal then Var (X) is


48) X : is number obtained on upper most free when a fair die ........... thrown then E(x) = ............


49) The expected value of the sum of two numbers obtained when two fair dice are rolled is .................


50) If E (x) = m and Var (x) = m then X follows ...............


51) If E (x) > Var (x) then X follows ...............


52) X is the number obtained on upper most face when a die is thrown then E(x) = 3.5.


53) If f(x) = k x (1 − x) for 0 < x < 1 = 0 otherwise then k = 12


54) If r.v. X assumes the values 1, 2, 3, ..........., 9 with equal probabilities, E(x) = 5.