Finite Chapter 7.6

Finite Chapter 7.6 - Math 120 SP08 SBrodnick 7.6: Bayes'...

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Math 120 SP08 SBrodnick 1 1 7.6 Applications 2 * A red dish and a green dish both contain blue and white poker chips. The probability of choosing the red dish is 0.40, and the probability of drawing a blue chip from the red dish is 0.70, whereas the probability of drawing a blue chip from the green dish is 0.60. Set up a probability tree to find a. P(B’|R) b. P(G B) c. P(B) d. P(G|B) 3 * Bayes’ Theorem (for two possibilities at each branch) P(A|T) = * You need Bayes’ Theorem when the “ given that event happens later on the tree, and you need to work backwards A A' T T' T T' P(T|A) · P(A) P(T|A) · P(A) + P(T|A') · P(A') 4 Examples : 1. Given the following tree, compute P(B|C). 2.For two events M and N, P(M) = 0.6, P(N|M) = 0.5, and P(N|M') = 0.2. Use Bayes’ Theorem to find a. P(M|N) b. P(M'|N) B B' C C' 0.2 0.7 C C' 0.9 0.8 0.3 0.1 5 3.For a fixed length of time, the probability of worker error on a certain production line is 0.06, the probability that an accident will occur
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Finite Chapter 7.6 - Math 120 SP08 SBrodnick 7.6: Bayes'...

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