NCERT Solutions for Class 11 Maths Chapter 16 Probability Ex 16.1

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

## 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 B1, B2 and G1, G2 are the boys and girls, respectively in room X, B3 and G3, G4, G5 are the boy and girls, respectively in room Y. The sample space of the experiment is as follows:
S = {XB1, XB2, XG1, XG2, YB3, YG3, YG4, YG5}

### 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 = {TR1, TR2, TB1, TB2, TB3, H1, H2, H3, H4, H5, H6}

### 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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