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Question 10: A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is 100. What is the probability that he will in a prize (a) at least once (b) exactly once (c) at least twice?Question 8: B | 6, NI- Suppose X has a binomial distribution . Show that X = 3 is the most likely outcome. (Hint: P(X = 3) is the maximum among all P (x,), x, = 0, 1, 2, 3, 4, 5, 6)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 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 5: The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs (i) none (ii) not more than one (lii) more than one (iv) at least one will fuse after 150 days of use.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?64 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 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 5 successes?Question 17: Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is 37 5 - 2 (A) 221 (B) 13 (C) 13 (D) 13Question 15: In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0 if he opposed, and X = 1 if he is in favour. Find E(X) and Var(X)