Probability

15. The possible outcome when a coin is tossed is a head or a tail. When a dice is thrown we can have the possible outcomes 1, 2, 3, 4, 5 and 6. Let R1, R2 be the two red balls and B1, B2, B3 be the two black balls. So, the desired sample space is

S = { (T, R1), (T, R2), (T, B1), (T, B2), (T, B3), (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}

14. The possible outcome when a coin is tossed is a head or a tail. When a die is thrown we can have the possible outcome 1, 2, 3, 4, 5 and 6. So, the desired sample space is

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

13. The possible numbers to be chosen are 1, 2, 3 and 4. The sample space of drawing two slips one after another without replacement 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)}

12. When a coin is thrown we have the possible outcome of a head or a tail. And when a dice is thrown we have the possible outcomes 1, 2, 3, 4, 5 and 6. So, the desired sample space is

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

11. Let us denote the non-defective and defective bulbs by 'N' and 'D'. So, that the sample space of selecting 3 bulbs from a lot is.

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

11. The possible outcomes when a coin is tossed is a Head or a Tail. And the possible outcomes when a die is rolled is 1, 2, 3, 4, 5 or 6.

By condition, when a head occurs or first toss the coin is tossed again and if a tail occurs on first toss a die is rolled. So, the required sample space is

S = { (H, H), (H, T), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5) and (T, 6)}

9. Let us denote the red and white balls by R and W. We are to draw one ball and then another ball without replacement. So, the desired sample space is

S = {RW, WR, WW}

8. Let us denote boys and girls by B and G.

(i) The desired sample space whether a boy or girl are the children according to their birth.

S = {BB, BG, GB, GG}

(ii) A family of two children can be two girls, one girl or no girl. So, the desired sample space is S = {0, 1, 2}

7. One rolling a dice we have the possible outcome 1, 2, 3, 4, 5 and 6. Let us denote R, W and B as red, white and blue respectively. So, the desired sample space 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)}

6. Let us denote B1, B2 to be the boys and G1, G2 to be the girls in Room X and B3 to be the boy and G3, G4, G5 to the girls in Room Y. Hence the desired sample space is

S = { (X, B1), (X, B2), (X, G1), (X, G2), (Y, B3), (Y, G3), (Y, G4), (Y, G5)}