# 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 2021-22 CBSE Second Term Examination, download in PDF format free based on NCERT Books 2021-2022.

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

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

### 11th Maths Chapter 16 Solutions in PDF

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 2021-2022. 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.

#### 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

##### Describe the sample space if a coin is tossed three times.

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

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}

##### Describe the sample space if a die is thrown two times.

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

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)}

##### One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.

A die has six faces that are numbered from 1 to 6, with one number on each face. Let us denote the red, white, and blue dices as R, W, and B respectively. 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}

##### An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

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

##### A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

In this experiment, six may come up on the first throw, the second throw, the third throw and so on till six is obtained. 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), …}

##### A die is rolled. Let E be the event “die shows 4” and F be the event “die shows even number”. Are E and F mutually exclusive?

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} It is observed that E ∩ F = {4} ≠ Φ Therefore, E and F are not mutually exclusive events.

##### How difficult the chapter 16 of class 11 Maths is?

Chapter 16 of class 11th Maths is overall an easy chapter. There are four exercises in chapter 16 of class 11th Maths. In the first exercise (Ex 16.1), there are 16 questions and 5 examples (1, 2, 3, 4, 5), the second exercise (Ex 16.2) has seven questions and three examples (6, 7, 8), the third exercise (Ex 16.3) contains 21 questions and five examples (9, 10, 11, 12, 13), In the last (Miscellaneous) exercise, there are ten questions and four examples (14, 15, 16, 17).

##### Which questions of chapter 16 of class 11th Maths are considered as the most important questions?

Chapter 16 of class 11th Maths has 54 questions and 17 examples. All problems of this chapter are important. But, the most important problems of this chapter that have chance to come in exams are questions 8, 11, 12, 14, 16 of exercise 16.1, questions 4, 6, 7 of exercise 16.2, questions 3, 4, 5, 7, 8, 11, 12, 14, 15, 16, 20, 21 of exercise 16.3, questions 4, 5, 7, 8, 9, 10 of miscellaneous exercise on chapter 16 and examples 2, 4, 5, 8, 9, 10, 12, 13, 14, 15, 17.

##### Can students complete chapter 16 of class 11th Maths in 1 week?

Students can complete chapter 16 of class 11th Maths in 1 week or not depends on many factors like student’s working speed, efficiency, capability, etc. But, if students seriously and honestly try to complete chapter 16 of class 11th Maths in 1 week (1 hour per day), they can easily do that because chapter 16 is an easy chapter.

##### What is the core motive of chapter 16 of class 11th Maths?

The core motive of chapter 16 of class 11th Maths is to teach students the following topics:

1. Random Experiments

2. Outcomes and sample space

3. Event

4. Occurrence of an event

5. Types of events (impossible and sure events, simple event, compound event)

6. Algebra of events

7. Complimentary event

8. The event ‘A or B’

9. The event ‘A and B’

10. The event ‘A but not B’

11. Mutually exclusive events

12. Exhaustive events

13. The axiomatic approach to probability

14. Probability of an event

15. Probabilities of equally likely outcomes

16. Probability of the event ‘A or B’

17. Probability of the event ‘not A’