HW1doc - Paul Gonzales 335 HW # 1 January 30, 2011 1. [24...

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Paul Gonzales 335 – HW # 1 January 30, 2011 1. [24 pts] Describe the following checkered regions using set notation: a) (A ∩ B) (B ∩ C) (A ∩ C) b) (A’ ∩ B ∩ C’) D c) (A ∩ D) (B ∩ D) (B ∩ E) (C ∩ E) 2. [20 pts] Consider the three sets (A, B and C) as shown in the figure below. The individual probabilities of the regions a through g are: P(a) = P(b) = P(c) = 0.2; P(d) = P(e) = P(f) = 0.1 and P(g) = 0.05. Find: P[(A C) (A B) (B C)]
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Paul Gonzales 335 – HW # 1 January 30, 2011 If we call the center region where A, B, C all intersect h then, P(a) + P(b) + P(c) + P(d) + P(e) + P(f) + P(g) + P(h) = 1 P(h) = 1- (P(a) + P(b) + P(c) + P(d) + P(e) + P(f) + P(g)) = 0.05 Then P[(A C) (A B) (B C)] = P(d) + P(e) + P(f) + P(h) = 0.1 + 0.1 + 0.1 + 0.05 = 0.35 3. [20 pts] The probability that team X wins a post season tournament is 1/6. The probability that the team X is the number one seed in the tournament is 1/12. If the
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HW1doc - Paul Gonzales 335 HW # 1 January 30, 2011 1. [24...

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