Appendix B

Answers to Selected Problems

Chapter 1

1. (a) {3, 4, . . ., 18} (b) [0, 1] × [0, 1] (c) {M, F} × {0, 1, 2, . . . }
(d) {(i, j): 1 ≤ i < j ≤ 10} (e) [0, 1].
2. S = {rr, rs, sr, ss}
3. (c) and (e)
4. (a) (ABcCc) ∪ (AcBCc) ∪ (AcBcC) (b) AcBcCc
(c) ABC
5. (a) B1 (b) img (c) B1B2B3B4
(d) imgimgimg
(e) img
6. 0.6
7. (a) P(B) = 0.4 (b, c) P(ABc) = 0.1 (d) P(Ac) = 0.7 (e) P(Bc) = 0.6
(f) P(AcBc) = 0.5 (which also equals P((AB)c)).537
8. (a) 0.5 − p (b) 1 − 2p (c) p
10. (b)
12. (a) 3/8 (b) 1/8 (c) 7/8 (d) 1/8 (e) 3/8
16. (a) 0.5 + 0.33 + 0.2 − (0.16 + 0.2 + 0.08) + 0.08 = 0.67
(b) P(Ai)+ P(Aj) + P(Ak) − (P(Alcm(i,j)) + P(Alcm(i,k)) + P(Alcm(j,k))) + P(Alcm(i,j,k)) (see Example 1.10)
17. (a) (7.1 + 15 − 0.75)/143 = 0.149
(b) (7.1 + 15 + 10 − (0.75 + 0.5 + 0) + 0)/143 = 0.216
(c) (71 + 15 + 71 + 1 − (7.5 + 35.5 + 0 + 7.5 + 0 + 0) + (3.75 + 0 + 0 + 0) − 0)/143 = 0.778
19. (a) (b)
20. (a) 23 × 22 × 21/233 = 0.87 (b) 10 × 9 × 8/103

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