# NCERT Solutions for Class 11 Maths Chapter 16

NCERT Solutions for Class 11 Maths Chapter 16 Probability all Exercises including miscellaneous exercise updated for new academic session 2020-21, download in PDF format free based on NCERT Books 2020-2021.

11th Maths Chapter 16 Exercise 16.1, Exercise 16.2, Exercise 16.3 and Miscellaneous Exercises in English Medium are given to study online.

## NCERT Solutions for Class 11 Maths Chapter 16

Class: | 11 |

Subject: | Maths |

Chapter 16: | Probability |

### 11th Maths Chapter 16 Solutions

NCERT Solutions for Class 11 Maths Chapter 16 Probability all exercises are given below to free download updated for new academic session 2020-2021. If you want to do class 12th without doing 11th class, go for NIOS Online Admission. Students studying in inter college, should also see Link Study Material Issued by CBSE.

### 11th Maths Chapter 16 Solutions in English Medium

### 11th Maths Chapter 16 Solutions in PDF

#### Important Questions on Probability

1. A coin is tossed. If it shows head, we draw a ball from a bag consisting of 2 red and 3 black balls. If it shows tail, coin is tossed again. [Answer: {HR1, HR2, HB1, HB2, HB3, TH, TT}]

2. Two balls are drawn at random in succession without replacement from a box containing 1 red and 3 identical white balls. [Answer: {RW, WR, WW}]

3. A coin is tossed n times. Find the number of element in its sample space. [Answer: 2^n]

4. One number is chosen at random from the numbers 1 to 21. What is the probability that it is prime? [Answer: 8/21]

5. What is the probability that a given two-digit number is divisible by 15? [Answer: 1/15]

##### Questions from Exam Papers

1. A game has 18 triangular block out of which 8 are blue and rest are red, and 19 square blocks out of which 7 are blue and rest are yellow. On piece is lost. Find the probability that it was a square of blue colour. [Answer: 1/4]

2. In a leap year find the probability of

(i) 53 Mondays and 53 Tuesdays

(ii) 53 Mondays and 53 Wednesday

(iii) 53 Mondays or 53 Tuesdays. [Answer: (i) 1/7, (ii) 0, (iii) 3/7]

3. In a non-leap year, find the probability of

(i) 53 Mondays and 53 Tuesdays.

(ii) 53 Mondays or 53 Tuesdays. [Answer: (i) 0, (ii) 2/7]

4. Two card are drawn at random from a deck of 52 playing cards. Find the probability of drawing two kings. [Answer: 1/221]

5. Find the probability that in a random arrangement of the letters of the word UNIVERSITY two I’s come together. [Answer: 1/5]

###### Questions for Practice

1. Out of 8 points in a plane 5 are collinear. Find the probability that 3 points selected at random form a triangle. [Answer: 23/28]

2. Find the probability of at most two tails or at least two heads in a toss of three coins. [Answer: 7/8]

### Important Questions on 11th Maths Chapter 16

When a coin is tossed three times, the total number of possible outcomes is 23 = 8

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

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

When 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 elements in this sample space is 6 × 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)}

Accordingly, when a die is selected and then rolled, the sample space is given by

S = {R1, R2, R3, R4, R5, R6, W1, W2, W3, W4, W5, W6, B1, B2, B3, B4, B5, B6}

A die has six faces that are numbered from 1 to 6, with one number on each face.

Thus, in the given experiment, the sample space is given by

S = {HH, HT, T1, T2, T3, T4, T5, T6}

Hence, the sample space of this experiment is given by

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

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

Accordingly, E = {4} and F = {2, 4, 6}

It is observed that E ∩ F = {4} ≠ Φ

Therefore, E and F are not mutually exclusive events.