# NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.1) Exercise 16.1

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## NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.1) Exercise 16.1

### Access NCERT Solutions for Class 11 Maths Chapter 16- Probability

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### Exercise 16.1

Exercise 16.1 contains 16 questions. These questions are based on the outcomes and sample space of an experiment. Some of the questions in the exercises can be confusing for the students. Students preparing for their yearly exams can benefit from the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 since they are prepared in simple language that all students can understand. In order to help students earn full marks on their exams, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 have been created in a stepwise manner. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 are developed in accordance with the most recent syllabus to avoid causing students to go elsewhere for the topics covered by the curriculum. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 comply with all CBSE guidelines. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 cover every question in the Class 11th Maths Chapter 16 Exercise 16.1 and are also completely error-free. Students can get ready for exams by using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 to assist them in quickly and accurately responding to questions like these. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 provided by Extramarks will be sufficient to help the students in answering the NCERT problems because they were written in an easy-to-understand manner. Students can apply the ideas from Class 11 Maths Exercise 16.1 more precisely and conveniently by using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1.

### NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.1

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Q.1 In each of the following Exercises 1 to 7, describe the sample space for the indicated experiment.

1. A coin is tossed three times.
2. A die is thrown two times.
3. A coin is tossed four times.
4. A coin is tossed and a die is thrown.
5. A coin is tossed and then a die is rolled only in case a head is shown on the coin.
6. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
7. 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.

Ans.

1. Sample space for a coin tossed three times is:
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

2. Sample space for a die thrown two times is:
{(x, y): x, y=1, 2, 3, 4, 5, 6} In other ways:

$\left\{\begin{array}{l}\left(1,\text{}1\right),\text{}\left(1,\text{}2\right),\text{}\left(1,\text{}3\right),\text{}\left(1,\text{}4\right),\text{}\left(1,\text{}5\right),\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(1,\text{}6\right)\\ \left(2,\text{}1\right),\text{}\left(2,\text{}2\right),\text{}\left(2,\text{}3\right),\text{}\left(2,\text{}4\right),\text{}\left(2,\text{}5\right),\text{}\left(2,\text{}6\right)\\ \left(3,\text{}1\right),\text{}\left(3,\text{}2\right),\text{}\left(3,\text{}3\right),\text{}\left(3,\text{}4\right),\text{}\left(3,\text{}5\right),\text{\hspace{0.17em}\hspace{0.17em}}\left(3,\text{}6\right)\\ \left(4,\text{}1\right),\text{}\left(4,\text{}2\right),\text{}\left(4,\text{}3\right),\text{}\left(4,\text{}4\right),\text{}\left(4,\text{}5\right),\text{\hspace{0.17em}\hspace{0.17em}}\left(4,\text{}6\right)\\ \left(5,\text{}1\right),\text{}\left(5,\text{}2\right),\text{}\left(5,\text{}3\right),\text{}\left(5,\text{}4\right),\text{}\left(5,\text{}5\right),\text{\hspace{0.17em}\hspace{0.17em}}\left(5,\text{}6\right)\\ \left(6,\text{}1\right),\text{}\left(6,\text{}2\right),\text{}\left(6,\text{}3\right),\text{}\left(6,\text{}4\right),\text{}\left(6,\text{}5\right),\text{\hspace{0.17em}\hspace{0.17em}}\left(6,\text{}6\right)\end{array}\right\}$

3. Sample space for a coin tossed four times is:

$\left\{\begin{array}{l}\mathrm{HHHH},\mathrm{HHHT},\mathrm{HHTH},\mathrm{HTHH},\mathrm{THHH},\mathrm{HHTT},\mathrm{HTTH},\mathrm{HTHT},\\ \mathrm{THHT},\mathrm{THTH},\mathrm{TTHH},\mathrm{TTTH},\mathrm{HTTT},\mathrm{TTHT},\mathrm{THTT},\mathrm{TTTT}\text{}\end{array}\right\}$

4. Sample space for a tossed coin thrown die is:

$\left\{\mathrm{H}\text{\hspace{0.17em}}1,\mathrm{H}\text{\hspace{0.17em}}2,\mathrm{H}\text{\hspace{0.17em}}3,\mathrm{H}\text{\hspace{0.17em}}4,\mathrm{H}5,\mathrm{H}\text{\hspace{0.17em}}6,\mathrm{T}1,\mathrm{T}2,\mathrm{T}3,\mathrm{T}4,\mathrm{T}5,\mathrm{T}6\right\}$

5. Sample space when a coin is tossed and then a die is rolled only when head is shown on the coin:

$\left\{\mathrm{H}\text{\hspace{0.17em}}1,\mathrm{H}\text{\hspace{0.17em}}2,\mathrm{H}\text{\hspace{0.17em}}3,\mathrm{H}\text{\hspace{0.17em}}4,\mathrm{H}5,\mathrm{H}\text{\hspace{0.17em}}6,\mathrm{T}\right\}$

6. The sample space for the experiment in which a room is selected and then a person is:

$\left\{{\mathrm{XB}}_{1},{\mathrm{XB}}_{2},{\mathrm{XG}}_{1},{\mathrm{XG}}_{2},{\mathrm{YB}}_{3},{\mathrm{YG}}_{3},{\mathrm{YG}}_{4},{\mathrm{YG}}_{5}\right\}$

7. Dice in red colour, white colour and blue colour are shown by R, W and B respectively. Then the required sample space is

$\left\{\mathrm{R}1,\mathrm{R}2,\mathrm{R}3,\mathrm{R}4,\mathrm{R}5,\mathrm{R}6,\mathrm{W}1,\mathrm{W}2,\mathrm{W}3,\mathrm{W}4,\mathrm{W}5,\mathrm{W}6,\mathrm{B}1,\mathrm{B}2,\mathrm{B}3,\mathrm{B}4,\mathrm{B}5,\mathrm{B}6\right\}$

Q.2 An experiment consists of recording boy–girl composition of families with 2 children.

(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?

Ans.
The boy and girl are represented by B and G respectively.
(i) The required sample space is:
{ BB,BG,GB,GG }

(ii) Sample space according to number of children in family is:
{ 0, 1, 2 }

Q.3 A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

Ans.
A red ball and white ball are represented by R and W respectively.
The required sample space is:
{ RW, WR, WW }.

Q.4 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.

Ans.
The head and tail are represented by H and T respectively.
The required sample space, when coin and die is thrown according to given condition, is:
{ HH, HT, T1, T2, T3, T4, T5, T6 }

Q.5 Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non – defective(N). Write the sample space of this experiment.

Ans.
The required sample space is:
{DDD, DDN, DND, NDD, DNN, NDN, NND, NNN}

Q.6 A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

Ans.
Sample space according to given conditions is:
{ T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66 }

Q.7 The numbers 1, 2, 3 and 4 are written separatly on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.

Ans.
The required sample space is:
{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}

Q.8 An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Ans.
The required sample space is:
{1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T }

Q.9 A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Ans.
The required sample space is:
{TR1, TR2, TB1, TB2, TB3, H1, H2, H3, H4, H5, H6}

Q.10 A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?

Ans.
Sample space when a die is thrown until a six is obtained.
{ 6, (1, 6), (2,6), (3,6), (4,6), (5,6), (1, 1, 6), (1, 2, 6), (1, 3, 6), (1, 4, 6), (1, 5, 6), (2,1,6), (2, 2, 6),…, (2,5,6), (3,1,6), (3, 2, 6), (3,3,6), (3, 4, 6), (3, 5, 6) …}