# 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 is 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) cube root of 217 is Show Answer

Q41) Which of the following is / are correct Show Answer

Q42) The value of least term in the expansion is Show Answer

Q43) The sum of odd numbered terms is Show Answer

Q44) Three consecutive binomial coefficient are given.
Statement I They cannot be in GP and HP.
Statement II They always are in AP. Show Answer

Q45) The binomial coefficients which are in decreasing order are Show Answer