Practice Test

Q1) A die is thrown 5 times. If getting an odd number is considered a success, then variance of the distribution is Show Answer

Q2) In tossing 10 coins, probability of getting exactly 5 heads is ... Show Answer

Q3) Probability that an event A happens in a trial is 0.4. If three independent trials are made, then probability that A happens at least once is Show Answer

Q4) Mean and variance of a binomial variate X are 4 and 2 respectively. Then P (X = 1) = ... Show Answer

Q5) Mean and variance of a binomial distribution are 4 and 2 respectively. Then probability of 2 successes is Show Answer

Q6) Mean and variance of a binomial variate X are 2 and 1 respectively. Then probability that X takes values greater than 1 is ... Show Answer

Q7) If 6 fair dice are rolled, then probability that at least half of them will show at least 3 is Show Answer

Q8) A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to the probability of getting 9 heads, then the probability of getting 2 heads is Show Answer

Q9) If a fair coin is tossed 5 times, then the probability of getting at least 5 heads is Show Answer

Q10) Workers in an industry have a 10% chance of suffering from an occupational disease. Probability that, out of 6 workers, at least 5 will catch the disease is Show Answer

Q11) As an answer to a question, two options are given only one of which is correct. Then the probability of correctly answering at least 6 of the 10 questions is ... Show Answer

Q12) If a fair coin is tossed 9 times, the probability that it shows heads in the first 4 tosses and tails in the last 5 tosses is ... Show Answer

Q13) If a coin is tossed n times, then probability that head will appear an odd number of times is Show Answer

Q14) Number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.95 us Show Answer

Q15) Each of two persons A and B tosses 3 fair coins. Probability that both get the same number of heads is Show Answer

Q16) If 10 coins are tossed simultaneously, then probability of getting at least 7 heads is Show Answer

Q17) If a fair coin is tossed 8 times, then probability that it shows heads more often than tails is Show Answer

Q18) If the chance of a gunshot hitting a target is 0.2, then the probability that at least 2 shots out of 10 will hit the target is Show Answer

Q19) Numbers are selected at random, one at a time, from the numbers 00, 01, 02, ..., 99, with replacement. An event A occurs if the product of the two digits of a selected number is 18. If 4 numbers are selected, then probability that A occurs at least 3 times is Show Answer

Q20) A boy is throwing stones at a target. Probability of hitting the target at any throw is 0.5. Probability of hitting the target 5th time at the 10th throw is Show Answer

Q21) From a box containing 20 tickets numbered 1 to 20, four tickets are drawn one by one. After each draw, the selected ticket is returned to the box. Then probability that the greatest number on the ticket drawn is 15 is Show Answer

Q22) In a box containing 100 bulbs, 64 are defective. Probability that, in a sample of 5 bulbs, none is defective, is Show Answer

Q23) Items produced by a company are supposed to contain 5% defective items. Probability that a sample of 8 items will contain less than 2 defective items is Show Answer

Q24) A binomial probability distribution is symmetrical, if the probability p is success in a single trial is Show Answer

Q25) If 5 coins are tossed simultaneously, then probability of at least one head is Show Answer

Q26) An experiment succeeds twice as often as it fails. Then probability that in the next six trials there are at least 4 successes is Show Answer

Q27) India plays 2 matches each with West Indies and Australia. In any match, probabilities of India getting 0, 1, 2 points are 0.45, 0.05, 0.50 respectively. If the outcomes are independent, then the probability of India getting at least 7 points is Show Answer

Q28) A die is thrown 100 times. If success is in getting an even number, then variance of number of successes is Show Answer

Q29) If turning up 1 or 3 is considered a success, then the S. D. of number of successes in 8 throws is Show Answer

Q30) A die is tossed 5 times. If getting an odd number is considered a success, then variance of the distribution of successes is Show Answer

Q31) In a box of 100 bulbs, 10 are defective. Then probability that, in a sample of 5, none is defective is Show Answer

Q32) A fair coin is tossed repeatedly. If the first 4 tosses show the same result, then probability that 5th toss shows a different outcome is Show Answer

Q33) A coin is tossed 2n times. Probability that number of heads is not equal to number of tails is Show Answer

Q34) Two cards are drawn successively, with replacement, from a well-shuffled deck of 52 cards. Then the mean of the number of aces is ... Show Answer

Q35) Sum of the mean and variance of a binomial distribution is 15. If the sum of their squares is 117, then the mean of the distribution is ... Show Answer

Q36) If 2 coins are tossed 5 times, the probability of getting an odd number of heads is Show Answer

Q37) An unbiased coin is tossed n times. If the probability that head occurs 6 times is equal to the probability that head occurs 8 times, then : n = ... Show Answer

Q38) A contest consists of predicting the results (win, draw or defeat) of 7 football matches. Then probability that an entry sent by Hemant based on his random predictions will contain exactly 4 correct predictions is Show Answer

Q39) If a coin is tossed 6 times, then probability of getting 4 or more heads is Show Answer

Q40) In the box containing 100 eggs 10 eggs are rotten the probablity that out of a sample of 5 eggs, none is rotten (if the sampling is with replacement) Show Answer

Q41) If two coins are tossed five times, then the probablity of getting 5 heads and 5 tails is Show Answer

Q42) The probability that an event A happens in one trial of the experiment is 0.4 . Three independent trials of the experiment are formed. The, probability that the event A happens atleast once is Show Answer

Q43) A radar complex consists of eight units that operate independently. The probablity that a unit detects an incoming missile is 0.9. Then the probablity that an incoming missile will not be detected by any unit is Show Answer

Q44) Five coins whose faces are marked 2, 3 are tossed. The chance of obtaining a total 12 is Show Answer

Q45) A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag. What is the probability that none is marked with the digit 0? Show Answer

Q46) A pair of dice is 4 times.If getting a doublet is considered a success, the probability of two successes isa Show Answer

Q47) On a multiple choice examination with three possible answer for each of five questions, what is the probability that a candidate would get four four or more correct answer just by guessing? Show Answer

Q48) India plays two matches each with the
West Indies and Australia. In any match, the probabilities of India getting 0, 1 and 2 points are 0.45, 0.05, and 0.50, respectively .Assuming that the outcomes are independent, the probability of India getting at least 7 points, is Show Answer

Q49) In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, all are defective is Show Answer

Q50) Unbiased coin is tossed 6 times. The probability of getting atmost 4 heads is Show Answer

Q51) A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tail is Show Answer

Q52) If in a trial the probability of success is twice the probability of failure. In the six trials the probability of at least four successes is Show Answer

Q53) A coin is tossed n times. The probability of getting head atleast once is greater than 0.8, then the least value of n is Show Answer

Q54) The records of a hospital show that 10% of the cases of a certain disease are fatal. If 6 patients are suffering from the disease, then the probability that only three will die, is Show Answer

Q55) In the four throws with a pair of dice, the chance of throwing doublets atleast twice is Show Answer

Q56) In an examination, 20 questions of true-false type are asked. Suppose a students tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers true, if it falls tails, he answers false. The probability that he answers atleast 12 questions correctly is Show Answer

Q57) The probability that a certain kind of component will survive a given shock test is 3/4. The probability that exactly 2 of the next 4 components testes survive is Show Answer

Q58) A dice is thrown 100 times. If getting an even number is considered a success, the variance of the number of successes, is Show Answer

Q59) The mean and variance of a random variable X having a binomial distribution are 4 and 2 respectively, then P(X=1),is Show Answer

Q60) In eight throws of a dice 1 and 3 is considered a success. Then, the standard deviation of success, is Show Answer

Q61) The mean and the variance of a binomial distribution are 4 and 2 respectively. Then, the probability of 2 successes is Show Answer

Q62) A dice is tossed 5 times. Getting an odd number is considered a success. Then, the variance of distribution of success is Show Answer

Q63) An unbiased coin is tossed n times. If the probability that head occurs 8 times is equal to the probability that head occurs 8 times, then n equals to Show Answer

Q64) A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. If it is thrown twice the probability that the sum of two numbers thrown is even, is Show Answer

Q65) A fair coin is tossed a fixed number of times. If the probability of getting 4 heads equals the probability of getting 7 heads, then the probability of getting 2 heads is Show Answer

Q66) An experiment succeeds twice as often as it fails.The probability that in the next six trials there are at most 2 success, is Show Answer

Q67) In a binomial distribution the mean is 15 and variance is 10. Then, parameter n is Show Answer

Q68) The mean and variance if binomial distribution are 4 and 3 respectively. Then, the probability of getting exactly six success in this distrubtion is Show Answer

Q69) The probability that a marksman will hit a target is given as 1/5. Then the probability that atleast one hit in 10 shots is Show Answer

Q70) A carton contains 20 bulbs, 5 of which are defective. The probability that, if a sample of 3 bulbs is chosen at random from the carton, 2 will be defective, is Show Answer

Q71) Out of 800 families with 4 children each, the expected number of families having atleast one boy is Show Answer

Q72) Five coins are tossed simultaneously. The probability that atleast one head turning up, is Show Answer

Q73) The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1, is Show Answer

Q74) A dice has four blank faces and two faces marked 3. The chance of getting a total of 12 in 5 throws is Show Answer

Q75) If a dice is thrown twice, the probability of occurrence of 4 atleast once is Show Answer

Q76) For a binomial variate X with n=6, if P(X=2)=9P(X=4), then its variance is Show Answer

Q77) A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is just one steps he is just one step away from the starting point, is Show Answer

Q78) The probability of India winning a test match against England is 2/3. Assuming independence from match to match, the probability that in a 7 match series India's third win occurs at the fifth match, is Show Answer

Q79) A man takes a forward step with probability (.8) and backward step with probability (.2). What is the probability that at the end of 9 steps he is exactly three steps away from starting points? Show Answer

Q80) If A and B each toss three coins. The probability that both get the same number of heads is Show Answer

Q81) A dice is thrown 5 times, then the probability that an even number will come up exactly 3 times is Show Answer

Q82) A dice is tossed thrice. If the event of getting an even number is a success, then the probability of getting atleast two successes is Show Answer

Q83) The probability that in a family of 5 members , exactly 2 members have birthday on sunday, is Show Answer

Q84) A fair dice is thrown twenty times. The probability that on the tenth throw the fourth six appears is Show Answer

Q85) If the mean and the variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes a value greater than or equal to one , is Show Answer

Q86) From a lot of 15 bulbs which include 5 defectives , a sample of 4 bulbs is drawn one by one with replacement . Find the mean of the number of defective bulbs Show Answer

Q87) Probability of guessing correctly atleast 7 out of 10 answers in a `true or false` test is equal to Show Answer

Q88) 15 coins are tossed, the probability of getting 10 heads will be Show Answer

Q89) If X follows the binomial distribution with parameters n=6 and p and 9p (X=4)=P(X=2), then p is Show Answer

Q90) Two coins are tossed simultaneously. Then, the value of E(X), where X denotes the number of heads is Show Answer

Q91) Mean and variance of a binomial distribution are 4 and 2 respectively. Then probability of 2 successes is Show Answer

Q92) A pair of fair dice is thrown independently three times. Then probability of getting a score of exactly 9 twice is Show Answer

Q93) Probability that an event A happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. Then probability that the event A happens at least once is Show Answer

Q94) One hundred identical coins, each with probability p of showing up heads, are tossed once.
If 0 < p < 1, and probability of heads showing upon 50 coins is equal to that of heads showing on 51 coins, then the value of p is Show Answer

Q95) A fair coin is tossed repeatedly. If the tail appears on first four tosses, then probability of head appearing on fifth toss is Show Answer

Q96) A die is thrown a fixed number of times. If probability of getting even number 3 times is equal to probability of getting even number 4 times, then probability of getting even number exactly once is Show Answer

Q97) A box contains 6 pens, 2 of which are defective. Two pens are taken randomly from the box. If r. v. x : Number of defective pens obtained, then standard deviation of x = Show Answer

Q98) It is observed that 25% of the cases related to child labour reported to the police station are solved. If 6 new cases are reported, then the probability that at least 5 of them will be solved is Show Answer

Q99) Out of 100 people selected at random, 10 have common cold. If five persons selected at random from the group, then the probability that at most one person will have common cold is Show Answer

Q100) If the sum of mean and variance of a binomial distribution for 5 trials is 1.8, then probability of a success is Show Answer