**NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1**

NCERT Solutions for Class
11 Maths Chapter 16
Probability Ex 16.1 are the part of NCERT Solutions for Class 11 Maths. Here
you can find the NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex
16.1.

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

**Ex 16.1 Class 11
Maths Question 1.**

A coin is tossed three times.

**Solution:**

If one coin is tossed three times, the sample space of the experiment is as
follows:

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

**Ex 16.1 Class 11
Maths Question 2.**

A die is thrown two times.

**Solution:**

If a die is thrown two times, the sample space of this experiment is as
follows:

S = {(1, 1), (1, 2), …, (1, 6), (2, 1), (2, 2), … (2, 6), …, (6, 1), (6, 2), …,
(6, 6)}

**Ex 16.1 Class 11
Maths Question 3.**

A coin is tossed four times.

**Solution:**

If a coin is tossed four times, the sample space of this experiment is as
follows:

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

**Ex 16.1 Class 11
Maths Question 4.**

A coin is tossed and a die is thrown.

**Solution:**

If a coin is tossed and a die is thrown, the sample space of the experiment is as
follows:

S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}

**Ex 16.1 Class 11
Maths Question 5.**

A coin is tossed and then a die is rolled only in case a head is shown on the
coin.

**Solution:**

If a coin is tossed and a die is rolled only in case a head is shown on the
coin, the sample space of the experiment is as follows:

S = {H1, H2, H3, H4, H5, H6, T}

**Ex 16.1 Class 11
Maths Question 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.

**Solution:**

Let B_{1}, B_{2} and G_{1}, G_{2} are
the boys and girls, respectively in room X, B_{3} and G_{3},
G_{4}, G_{5} are the boy and girls, respectively in room
Y. The sample space of the experiment is as follows:

S = {XB_{1}, XB_{2}, XG_{1}, XG_{2}, YB_{3},
YG_{3}, YG_{4}, YG_{5}}

**Ex 16.1 Class 11
Maths Question 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.

**Solution:**

Let R, W and B denote the red, white and blue dice, respectively. The sample
space S, for this experiment is as follows:

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

**Ex 16.1 Class 11
Maths Question 8.**

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?

**Solution:**

**(i)** The
sample space S, in knowing whether it is a boy or a girl in the order of their
births in composition of families with two children is: S = {BB, BG, GB, GG}.

**(ii)** The
sample space S, in knowing the number of girls in a family is: S = {0, 1, 2}.

**Ex 16.1 Class 11
Maths Question 9.**

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.

**Solution:**

There are 1 red and 3 identical white balls in the box. The sample space of
this experiment is as follows:

S = {RW, WR, WW}

**Ex 16.1 Class 11 Maths Question
10.**

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.

**Solution:**

The sample space S, for tossing a coin and then throwing it second time if a
head occurs; if a tail occurs on the first toss, the die is tossed once is as
follows:

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

**Ex 16.1 Class 11
Maths Question 11.**

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.

**Solution:**

The sample space S for selecting three bulbs at random from a lot is:

S = {DDD, DDN, DND, NDD, DNN, NDN, NND, NNN}

**Ex 16.1 Class 11
Maths Question 12.**

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?

**Solution:**

An experiment consists of tossing a coin. If the outcome is a head, a die is
thrown. If the die shows up an even number, the die is thrown again. The sample
space of this experiment as follows:

S = {T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46,
H61, H62, H63, H64, H65, H66}

**Ex 16.1 Class 11
Maths Question 13.**

The numbers 1, 2, 3 and 4 are written separately 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.

**Solution:**

Four slips written as 1, 2, 3 and 4 are put in a box. Two slips are drawn from
it one after the other without replacement. The sample space S, for this
experiment is

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

**Ex 16.1 Class 11
Maths Question 14.**

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.

**Solution:**

An experiment consists of rolling a die and then tossing a coin once if the
number on the die is even. If the number is odd, the coin is tossed twice. The
sample space of this experiment is as follows:

S = {1HH, 1TH, 1HT, 1TT, 2H,
2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T}

**Ex 16.1 Class 11
Maths Question 15.**

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.

**Solution:**

An experiment consists of tossing a coin. If it shows a tail, a ball is drawn
from a box which contains 2 red and 3 black balls. If it shows head, a die is
thrown. Then, the sample of this experiment is follows:

S = {TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3},
H_{1}, H_{2}, H_{3}, H_{4}, H_{5}, H_{6}}

**Ex 16.1 Class 11
Maths Question 16.**

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

**Solution:**

An experiment consists of rolling a die. The sample space for this experiment
is as follows:

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

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