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Assignment 3 Solutions

Assignment 3 Solutions - CE93-Engineering Data Analysis...

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CE93-Engineering Data Analysis Joan Walker, Spring 2011 Assignment 4 Solutions 1. (30 Points) Earthquakes and tidal waves Define everything: Probability of earthquake = P(E) = 0.1 Probability of eastbound tidal wave given that earthquake happens = P(T E |E) = 0.04 Probability of westbound tidal wave given that earthquake happens = P(T W |E) = 0.05 Probability of westbound tidal wave given eastbound tidal wave occurs = P(T W |T E ) = 0.15 Probability of damage to Mauritius = P(D M ) Probability of damage to Australia = P(D A ) a) (10 points, 5 for formulation, 5 for answer) 𝑃 ? 𝑀 = 𝑃 ? 𝑊 ∩ ? = 𝑃 ? 𝑊 ? ∗ 𝑃 ? = 0.05 0.01 = 0.005 = 0.5% (last year was 0.4%) b) (20 point, 15 for formulation, 5 for answer) 𝑃 ? ? ∪ ? 𝑀 = 𝑃 ? ? + 𝑃 ? 𝑀 − 𝑃 ? ? ∩ ? 𝑀 = 𝑃 ? ? ∩ ? + 𝑃 ? 𝑊 ∩ ? − 𝑃 ? 𝑊 ∩ ? ? ∩ ? = 𝑃 ? ? ∩ ? + 𝑃 ? 𝑊 ∩ ? − 𝑃 ? 𝑊 ∩ ? ? = 𝑃 ? ? ∩ ? + 𝑃 ? 𝑊 ∩ ? − 𝑃 ? 𝑊 | ? ? ∗ 𝑃 ? ? = 𝑃 ? ? ∩ ? + 𝑃 ? 𝑊 ∩ ? − 𝑃 ? 𝑊 | ? ? ∗ 𝑃 ? ? | ? ∗ 𝑃 ? = 0.004 + 0.005 0.15 0.04 0.1 = 0.0084 𝑜𝑟 0.84% 2. (20 Points) A: the event that a radio was produced at factory A
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