QUIZ 1-1 - 0.25 ⋅ 0.60 0.15 0.10 0.25 No Rain Monday M '...

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STAT 400 Spring 2011 Version A Name ANSWERS . Quiz 1 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. A local meteorologist noticed that if it rains on Monday, then the probability that it also rains on Tuesday is 0.60. However, if it does not rain on Monday, then the probability that it rains on Tuesday is only 0.20. Suppose that the probability that it rains on Monday is 0.25. M = {Rain Monday}, T = {Rain Tuesday}. P(T | M) = 0.60, P(T | M ' ) = 0.20, P(M) = 0.25. a) (4) What is the probability that it rains on Tuesday? P(T) = P(M T) + P(M ' T) = P(M) P(T | M) + P(M ' ) P(T | M ' ) = 0.25 0.60 + 0.75 0.20 = 0.15 + 0.15 = 0.30 . OR Rain Tuesday T No Rain Tuesday T ' Total Rain Monday M
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Unformatted text preview: 0.25 ⋅ 0.60 0.15 0.10 0.25 No Rain Monday M ' 0.75 ⋅ 0.20 0.15 0.60 0.75 Total 0.30 0.70 1.00 OR P(T) = 0.15 + 0.15 = 0.30 . b) (2) Suppose one week it rained on Tuesday. What is the probability that it also rained on Monday? P(M | T) = 30 . 15 . P(T) T) P(M = ∩ = 0.50 . c) (2) What is the probability that it did not rained on Monday, if it did not rained on Tuesday? P(M ' | T ' ) = 7 6 = = ∩ 70 60 ) P(T ) T P(M . . ' ' ' ≈ 0.8571 . d) (2) What is the probability that it rains either on Monday or on Tuesday, or both? P(M ∪ T) = P(M) + P(T) -P(M ∩ T) = 0.25 + 0.30 -0.15 = 0.40 . OR P(M ∪ T) = P(M ∩ T) + P(M ∩ T ' ) + P(M ' ∩ T) = 0.15 + 0.10 + 0.15 = 0.40 . OR P(M ∪ T) = 1 – P(M ' ∩ T ' ) = 1 – 0.60 = 0.40 ....
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This note was uploaded on 11/28/2011 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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QUIZ 1-1 - 0.25 ⋅ 0.60 0.15 0.10 0.25 No Rain Monday M '...

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