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

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 13. Probability

Subject: Maths - Class 12^th

Q. No. 15 of Exercise 13.5

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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

In this question, let us assume X represent the number of students out of 5 who are swimmers

Also, the repeated selection of students who are swimmers are the Bernoulli trials

Thus, probability of students who are not swimmers

Clearly, we have X has the binomial distribution where n = 5

And,

∴

_{Hence, probability that four students are swimmers = P (X = 4)}

∴ option A is correct

15

Chapter Exercises

Exercise 13.1

Exercise 13.2

Exercise 13.3

Exercise 13.4

Exercise 13.5

Miscellaneous Exercise

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?

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 more than one

(iii) more than one

(iv) at least one will fuse after 150 days of use.

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?

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.

8

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)

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 ?

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?

11

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

12

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

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?

14

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

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