Practice Test


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


2) In tossing 10 coins, probability of getting exactly 5 heads is ...


3) 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


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


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


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


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


8) 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


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


10) 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


11) 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 ...


12) 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 ...


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


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


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


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


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


18) 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


19) 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


20) 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


21) 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


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


23) 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


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


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


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


27) 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


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


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


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


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


32) 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


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


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


35) 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 ...


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


37) 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 = ...


38) 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


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


40) cube root of 217 is


41) Which of the following is / are correct


42) The value of least term in the expansion is


43) The sum of odd numbered terms is


44) Three consecutive binomial coefficient are given.
Statement I They cannot be in GP and HP.
Statement II They always are in AP.


45) The binomial coefficients which are in decreasing order are