# NCERT Solutions for Class 11 Maths Chapter 16 Probability

## NCERT Solutions Class-11 Maths Chapter 16 Probability

The academic team at Physics Wallah has developed comprehensive, step-by-step NCERT Solutions for Class 11 Maths, Chapter 16: Probability (Exercise 16.1, 16.2, 16.3), in accordance with the guidelines and recommendations set by CBSE. Before attempting the exercises, ensure you have thoroughly reviewed the theory section of Chapter 16: Probability from the NCERT textbook and are familiar with the relevant formulas. You can download and share these NCERT Solutions for Class 11 Maths.

## NCERT Solutions for Class 11Maths chapter 16 Exercise 16.1

### EX 16.1 Class 11 Maths Question 1:

Describe the sample space for the indicated experiment: A coin is tossed three times.

**Ans:**

A coin has two faces: head (H) and tail (T).

Wehen a coin is tossed times, the total numbers of possible outcomes is 2^{3} = 8

Thus, when a coin is tissed three, the sample space is given by:

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

### EX 16.1 Class 11 Maths Question 2:

Describe the sample space for the indicated experiment: A die is thrown two times.

**Ans:**

When a die is thrown, the possible outcomes are 1, 2, 3, 4, 5, or 6.

Wehen a die is thrown two times, the sample space is given by S = {(x, y): x, y = 1, 2, 3, 4, 5, 6}

The number of elemets in this sample space is 6 x 6 = 36, while the sample space is given by:

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}

### EX 16.1 Class 11 Maths Question 2:

Describe the sample space for the indicated experiment: A coin tossed four times.

**Ans:**

When a coin is tossed once, there are two possible outcomes: head (H) and tail (T).

Wehen a coin is tossed four times, the total number of possible out comes is 2^{4} = 16

Thus, When a coin is tossed four times, the sample space is given by:

S = {HHHH, HHHT, HHTH, HHTT, HTHT, HTTH, THHH, THHT, THTH, THTT, TTHH, TTHT, TTTH, TTTT}

## NCERT Solutions for Class 11Maths chapter 16 Exercise 16.2

### EX 16.2 Class 11 Maths Question 1:

A die is rolle. Let E be the event "die shows 4" and F be the event "die shows even number". Are E and F mutually exclusive?

**Ans:**

When a die is rolled, the sample space is given by

S = {1, 2, 3, 4, 5, 6}

Accordingly, E = {4} and f + {2, 4, 6}

### EX 16.2 Class 11 Maths Question 2:

A die is thrown. Describe the following events:

(i) A: a number less than 7 (ii) B: a number greater than 7 (iii) C: a multiple of 3

(iv) D: a number less than 4 (v) E: an even number greater than 4 (vi) F: a number not less than 3

### EX 16.2 Class 11 Maths Question 3:

An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:

A: the sum is greater than 8, B: 2 occurs on either die

C: Thesum is at leas 7 and a multiple of 3.

Which pairs of these events are mutually exclusive?

**Ans:**

When a pair of dice is rolled, the sample space is given by

## NCERT Solutions for Class 11Maths chapter 16 Exercise 16.3

### EX 16.3 Class 11 Maths Question 1:

Which of the following can not be valid assignment of probabilities for outcomes of

### EX 16.3 Class 11 Maths Question 2:

A coin is tossed twice, what is the probability that at least one tail occurs?

**Ans:**

When a coin is tossed twice, the sample space is given by

S = {HH, HT, TH, TT}

Let A be the vent of the occurrence of at least tail.

Accordingly,A = {HT, TH, TT}

## Class 11 Maths NCERT Solutions - Miscellaneous Questions

### Miscellaneous Exercise Class 11 Maths Question-1

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn from the box, what is the probablility that

(i) all will b blue? (ii) atleast one will be green?

**Ans:**

Total number of marbles = 10 + 20 + 30 = 60

Number of ways of drawing 5 marbles from 60 marbles = ^{60}C_{5}

(i) all the drawn marbles will be blue if we draw 5 marbles out of 20 blue marbles.

### Miscellaneous Exercise Class 11 Maths Question-2

4 cards are drawn from a well-shuffled deck of 52 cards. What is the probablility of obtaining 3 diamonds and one spade?

**Ans:**

Number of ways of drawing from 52 cards = ^{52}C_{4}

In a deck of 52 cards, there are 13 diamonds and 13 spades.