Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 16 Probability Ex 16.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 16 Probability Ex 16.1

In each of the following questions 1 to 7, describe the sample space for the indicated experiment:

Question 1.

A coin is tossed three times.

Solution:

When one coin is tossed three times, the possible outcomes of the experiment are HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

∴ The sample space is given by

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

Question 2.

A die is thrown two times.

Solution:

When a die is thrown two times, the sample space S for this experiment is given by

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

Question 3.

A coin is tossed four times.

Solution:

When a coin is tossed four times. The sample space S associated with this experiment is

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

Question 4.

A coin is tossed and a die is thrown.

Solution:

When a coin is tossed and a die is thrown, the sample space S associated with experiment is .

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

Question 5.

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

Solution:

When a coin is tossed and a die is rolled only in case a head is shown on the coin. The sample space S associated with experiment is

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

Question 6.

2 boys and 2 girls are in Room X and 1 boy and 3 girls are 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 in room X, B_{3} and G_{3}, G_{4}, G_{5} are the boy and girls in room Y.

The sample space S for the experiment in which a room is selected and then a person is

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

Question 7.

One die of red colour, one white 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. The sample space S for the selection of on die at random and rolling is

S = {R_{1}, R_{2}, R_{3}, R_{4}, R_{5}, R_{6}, W_{1}, W_{2}, W_{3}, W_{4}, W_{5}, W_{6}, B_{1}, B_{2}, B_{3}, B_{4}, B_{5}, B_{6}}.

Question 8.

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

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

Solution:

1. The sample space S in knowing whether it is a boy or girl in the order of their birth in composition of families is given by

S = {BB, BG, GB, GG}

2. The sample space S in knowing the number of girls in a family is given by

S = {0, 1, 2}

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 a box. The sample space S for selected two balls at random in succession without replacement is

S = {RW, WR, WW}.

Question 10.

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

Solution:

The sample space S, for tossing a coin and then tossing it second time, if a head occurs, if a tail occurs on the first toss, the die is tossed once is given by

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

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, DNN, NDD, NDN, NND, NNN},

where D indicates a defective bulb and N a non-defective bulb.

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 this experiment?

Solution:

A coin is tossed. If the result is a head, a die is thrown. If the die shows up an even number, the die is thrown again. The sample space S for this experiment is

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

Question 13.

The number 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then 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 marked as 1, 2, 3 and 4 are in a box. Two slips are drawn from it one after the other without replacement. The sample space S, for the experiment, is given by

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)}.

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 consisting 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 S for this experiment is given by

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

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. Sample space for this experiment is

S = {TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}, H1, H2, H3, H4, H5, H6)

Question 16.

A die is thrown repeatedly until 6 conies up. What is the sample space for the experiment?

Solution:

Let N denotes the event that 6 does not appear.

∴ Sample space = {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), ……………}