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?

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

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?

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?

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.

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?

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.

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(xi), xi = 0,1,2,3,4,5,6)

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 ?

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?

Find the probability of getting 5 exactly twice in 7 throws of a die.

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

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 a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is

The probability that a student is not a swimmer is 1/5. Then the probability that out of five students, four are swimmers is