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c Math 166 WIR, Spring 2011, Benjamin Aurispa Math 166 Exam 1 Review Answer Key 1. (a) P (c) = 0.18, P (e) = 0.15 (b) 0.34 (c) 0.67 (d) 0.85 (e) No, not all outcomes are equally likely. 2. (a) 0.3 (b) 0.6 (c) 0.7 (d) 0.1 (e) No, since P (E ∩ F ) 6= 0, or equivalently, E ∩ F 6= ∅ (f) No, since P (E ∩ F ) 6= P (E)P (F ) 3. 0.76 32 40 16 40 12 40 4. (a) (b) (c) = = = 4 5 2 5 3 10 (d) 1 to 7 5. 90 92 = 6. (a) (b) (c) 45 46 10 5 36 = 18 1 3 6 = 2 7 11 7. (a) 0.2 (b) 0.54 (c) 0 (d) 0.86 (e) 0.94 8. (a) (b) 330 33 350 = 35 30 1 60 = 2 (c) Not independent since P (G ∩ U ) 6= P (G)P (U ) 9. 54 1033 ≈ 0.0523; See Full Solutions for Tree Diagram 10. See Full Solutions for Tree Diagram (a) 0.7092 (b) 0.85 (c) 22 727 ≈ 0.0303 11. (a) 0.000189 1 c Math 166 WIR, Spring 2011, Benjamin Aurispa (b) 0.168367 12. See Full Solutions for Tree Diagram (a) (b) 4 15 27 47 ≈ 0.5745 13. (a) The set of all residents in College Station who were born in Texas and are students at TAMU, or who do not attend TAMU but are at least 21 years old. (b) B ∩ Ac ∩ T c 14. Shade regions b, c, and h 15. a = 110, b = 90, c = 135, d = 165 (a) (b) 335 500 275 500 = = 67 100 11 20 (c) YES, P (D ∩ F ) = P (D)P (F ) 16. a = 30, b = 16, c = 26, d = 10, e = 25, f = 17, g = 29, h = 32 (a) 46 (b) 85 (c) 69 185 Size Probability 17. (a) (b) 525 900 18. (a) i. ii. iii. iv. v. vi. vii. viii. = S M L XL XXL 150 950 225 950 300 950 200 950 75 950 21 38 True False False True False False True False i. {b, c, f, g, i} ii. {a, b, f, i, j} (b) 19. (a) S = {Hh, Ht, Ch, Ct, D1, D2, D3, D4, S} (b) E = {Ch, Hh} (c) F = {D1, D3} (d) G = {Ch, Ct, S} (e) E and F are mutually exclusive; F and G are mutually exclusive (f) 20. (a) 1 4 i. The average temperature in August is 95◦ and it either rained 10 days in August or August does not have the highest monthly average temperature. 2 c Math 166 WIR, Spring 2011, Benjamin Aurispa ii. It did not rain 10 days in August, or both the average temperature in August is 95◦ and August has the highest monthly average temperature. (b) i. ∼ (r ∨ q) ∧ p ii. (p ∧ ∼ r) Y q 21. (a) p q (∼ p ∧ q)∨ ∼ q T T F T F T F T T F F T p q r (p Y ∼ q)∧ ∼ (q ∨ r) T T T F T T F F T F T F T F F F F T T F F T F F F F T F F F F T (b) 3