Q. 5 An urn contains balls of which balls bear a mark and the remaining bear a mark A ball is drawn at random from the urn, its mark is noted down and it is replaced. If balls are drawn in this way, find the probability that
(i) all will bear mark.
Q. 4 Suppose that of people are right-handed. What is the probability that at most of a random sample of people are right-handed?
Q. 3 Suppose that of men and of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
Q .2 A couple has two children,
(ii) Find the probability that both children are females, if it is known that the elder child is a female.
Q. 2 A couple has two children,
(i) Find the probability that both children are males, if it is known that at least one of the children is male.
Q. 15 The probability that a student is not a swimmer is Then the probability that out of five students, four are swimmers is
In the following, choose the correct answer:
(D) None of these
Q. 14 In a box containing bulbs, are defective. The probability that out of a sample of bulbs, none is defective is
Q. 13 It is known that of certain articles manufactured are defective. What is the probability that in a random sample of such articles, are defective?
Q. 10 A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is . What is the probability that he will win a prize
(c) at least twice?
Q. 10 A person buys a lottery ticket in lotteries, in each of which his chance of winning a prize is . What is the probability that he will win a prize
(b) exactly once
Q. 10 A person buys a lottery ticket in lotteries, in each of which his chance of winning a prize is What is the probability that he will win a prize
(a) at least once
Q. 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 ?
Q. 8 Suppose X has a binomial distribution Show that is the most likely outcome.
(Hint : is the maximum among all of , )
Q. 7 In an examination, 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.
Q. 6 A bag consists of balls each marked with one of the digits to If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit ?
Q. 5 The probability that a bulb produced by a factory will fuse after days of use is . Find the probability that out of such bulbs
(iv) at least one will fuse after days of use.