C: ANSWERS TO SELECTED PROBLEMS

Chapter 4.1, Basic Concepts

1. 3.

5. 7.

9. 11.

13.

15.

17. 19.

21.

23.

25. Pick 1 of 4 suits, then pick 5 cards in that suit,

.

27. Pick 1 of the 4 suits, there are 9 such sequences in each suit,

29.

Chapter 4.2, Conditional Probability and Independence

1.

3.

5.

7.

9.

11. 0.08.

13.

15. Not independent, 0.001, 9 times. 17. 0.42.

19.

21. [a] Pr[2R] = 0.05 + 0.03125 = 0.08125, [b] Pr[at least 1 R] = 0.56875.

23.

25. [a] 21/44, [b] 6/11.

27. [a] 4/52, [b] 13/51, [c] 16/2,652.

29. 0.4148. 31. [a] 0.20, [b] 0.2667, [c] 0.45.

Chapter 4.3, Bayes' Probability

1. .

3. .

5.

7. 9.

11. 0.375.

13. 15.

17. 19.

21. 23.

25. 27. 1/3.

Chapter 4.4, Bernoulli Trials

1. 0.2373. 3. 0.1977.

5. 0.2254. 7.

9. [a] , [b]

11.

13. 15. 0.0026.

17. 19. Find smallest n,

21. 0.1316. 23. [a] 0.1509, [b] 0.8814.

25. is most likely, then , and least likely

27. 14. 29. 4.

Chapter 4.5, Chapter Review

Mastery Quiz

1. [b], 2. [b], 3. [b], 4. [d], 5. [a], 6. [c], 7. [d], 8. [c], 9. [c], 10. [b]

Review

1. [a] .6, [b] .12, [c] .2, [d] 0. 3. [a] 3/8, [b] 3:5, [c] 5:3.

5. 0.375. 7. 0.6.

9. 3/13.

11. Pick 2 ranks, then 1 of 2 for triple, pick 3 cards, pick 2 cards,

.

13. .

15. 0.0698. 17. 0.2.

19. 20/21. 21. 0.7.

23. 0.1.

25.

27.

29. 1/120. 31. [a] 1/201 [b] 3/250,003 [c] 3/500,003.