*In each of the following Exercises 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 sample space of the experiment 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 for this experiment is given by

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 for the experiment is given by

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 the case ahead is shown on the coin.**

**Solution:**

When a coin is tossed and a die is rolled only in case if the head is shown on the coin. The sample space S for the experiment is given by

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 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 S for the experiment is given by

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

**Question 7.**

**One die of red color, one of white color and one of blue color are placed in a bag. One die is selected at random and rolled, its color 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 given by

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

**Question 8.**

**An experiment consists of recording the 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 the 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}.

**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 this experiment is given by S = {RW, WR, WW}.

**Question 10.**

**An experiment consists of tossing a coin and then throwing it a 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 tossing it a 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 is 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}.

**Question 12.**

**A coin is tossed. If the outcome is ahead, 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 result is ahead**, a die is thrown. If the die shows up as 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, H45, H46, H61, H62, H63, H64, H65, H66}.

**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 marked 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 the 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)}.

**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 S for this experiment is given by S = {1HH, 1TH, 1HT, 1TT, 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 that 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 that contains 2 red and 3 black balls. If it shows head, a die is thrown. Then the sample S for this experiment is given by

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

**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.

∴ 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),…}.