1. A die is thrown 6 times. If getting an odd number is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most 2. A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes. 3. There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item? 4. Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade? 5. The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs (i) none (ii) not mor
Question 1:A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of (i) 5 successes? (ii) at least 5 successes? (iii) at most
Question 2:A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
Question 3:There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?
Question 4:Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
Question 5:The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs (i) none (ii) not more than one (iii) more than one (iv) at least one will fuse after 150 days of use.
Question 6: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?
Question 7:In an examination, 20 questions of true-false type are asked. Suppose a student 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'. Find the probability that he answers at least 12 questions correctly.
Question 8:Suppose X has a binomial distribution 1 B 6, 2 . Show that X = 3 is the most likely outcome. (Hint : P(X = 3) is the maximum among all P(x i ), x i = 0,1,2,3,4,5,6)
Question 9:On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?
Question 10:A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 1 100 . What is the probability that he will win a prize (a) at least once (b) exactly once (c) at least twice
Question 11:Find the probability of getting 5 exactly twice in 7 throws of a die.
Question 12:Find the probability of throwing at most 2 sixes in 6 throws of a single die.
Question 13:It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective? In each of the following, choose the correct answer:
Question 14:In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is (A) 10–1 (B) 5 1 2 (C) 5 9 10 (D) 9 10
Question 15:The probability that a student is not a swimmer is 1 . 5 Then the probability that out of five students, four are swimmers is (A) 4 5 4 4 1 C 5 5 (B) 4 4 1 5 5 (C) 4 5 1 1 4 C 5 5 (D) None of these
