1. Chapter 11 Section 11.2 Exercise #1

2. Using the sample space for the genders of three children in the family shown in Example 11-4, find the following probabilities.

3. Outcomes B BBB B BBG G B BGB B G BGG G GBB B B G GBG G GGB B 1st child G 2nd child G GGG 3rd child

4. Sample space = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} There are 8 outcomes, so n(S) = 8. a) The probability that the family will have exactly two girls:

5. Sample space = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} There are 8 outcomes, so n(S) = 8. b) The probability that the family will have three boys:

6. Sample space = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG} There are 8 outcomes, so n(S) = 8. c) The probability that the family will have at least one girl:

7. Chapter 11 Section 11.2 Exercise #5

8. A box contains a one-dollar bill, a five-dollar bill, and a ten-dollar bill. A bill is selected and its value is noted, then it is replaced in the box. A second bill is then selected. Draw the tree diagram to determine the sample space, and find the following probabilities.

9. Outcomes 1 1, 1 1, 5 5 1 1,10 10 1 5, 1 5 5 5, 5 10 5, 10 1 10, 1 10 5 10, 5 10 10, 10

10. Sample space ={1,1 ; 1,5 ; 1,10 ; 5,1 ; 5,5 ; 5,10 ; 10,1 ; 10,5 ; 10,10} There are 9 outcomes, so n(S) = 9. a) The probability that both bills have the same value:

11. Sample space ={1,1 ; 1,5 ; 1,10 ; 5,1 ; 5,5 ; 5,10 ; 10,1 ; 10,5 ; 10,10} There are 9 outcomes, so n(S) = 9. b) The probability that the second bill is larger than the first bill:

12. Sample space ={1,1 ; 1,5 ; 1,10 ; 5,1 ; 5,5 ; 5,10 ; 10,1 ; 10,5 ; 10,10} There are 9 outcomes, so n(S) = 9. c) The probability that each of the two bills is even:

13. Sample space ={1,1 ; 1,5 ; 1,10 ; 5,1 ; 5,5 ; 5,10 ; 10,1 ; 10,5 ; 10,10} There are 9 outcomes, so n(S) = 9. d) The probability the value of exactly one of the bills is odd:

14. Sample space ={1,1 ; 1,5 ; 1,10 ; 5,1 ; 5,5 ; 5,10 ; 10,1 ; 10,5 ; 10,10} There are 9 outcomes, so n(S) = 9. e) The probability the sum of the value of both bills is less than $10 :

15. Chapter 11 Section 11.2 Exercise #7

16. Mark and Bill play a chess tournament consisting of three games. They are equal in ability. Draw a tree diagram to determine the sample space, and find the following probabilities.

17. Outcomes M MMM M MMB B M MBM M B MBB B BMM M M B BMB B BBM M 1st game B 2nd game B BBB 3rd game

18. Sample space = {MMM, MMB, MBM, MBB, BMM, BMB, BBM, BBB} There are 8 outcomes, so n(S) = 8. a) The probability that either Mark or Bill win all three games:

19. Sample space = {MMM, MMB, MBM, MBB, BMM, BMB, BBM, BBB} There are 8 outcomes, so n(S) = 8. b) The probability that either Mark or Bill win two out of three games:

20. Sample space = {MMM, MMB, MBM, MBB, BMM, BMB, BBM, BBB} There are 8 outcomes, so n(S) = 8. c) The probability that Mark wins only two games in a row:

21. Bill wins first, loses second, wins third Sample space = {MMM, MMB, MBM, MBB, BMM, BMB, BBM, BBB} There are 8 outcomes, so n(S) = 8. d) The probability that Bill wins the first game, loses the second game, and wins the third game:

22. Chapter 11 Section 11.2 Exercise #13

23. Using the sample space for drawing asingle card from an ordinary deck of 52 cards, find the following probabilities.

24. a) The probability of getting a 10:

25. b) The probability of getting a club:

26. c) The probability of getting an ace of hearts:

27. d) The probability of getting a 3 or a 5:

28. e) The probability of getting a 6 or a spade:

29. f) The probability of getting a queen or a club:

30. g) The probability of getting a diamond or a club:

31. h) The probability of getting a red king: