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10 Bayes HW3 Exam - Example 2 Your birthday is coming up...

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1/5/10 Example 2 Your birthday is coming up, and you are afraid that your wife might be planning a surprise party for you. In the past she has thrown you a surprise party on 10% of your birthdays. However, you know that if she is going to throw a party, there is an 80% she won’t make eye contact with you the day before. If she is not going to throw a party, there is only a 30% chance of no eye contact.
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1/5/10 Probability Tree for Ex.2 P(S) = .1 P(S’) = .9 P(Ec| S’) =.7 P(Ec’| S’) =.3 P(Ec| S) =.2 P(Ec’| S) =.8 Given P(Ec’|S) = 0.8 in the problem description. Since Ec and Ec‘ are exhaustive and by definition M.E., P(Ec’|S) = 1 - P(Ec|S)
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1/5/10 Probability Tree for Ex.2 P(S) = .1 P(S’) = .9 P(Ec| S’) =.7 P(Ec’| S’) =.3 P(Ec| S) =.2 P(Ec’| S) =.8 P(Ec|S)P(S) = P(Ec ° S) P(Ec|S’)P(S’) = P(Ec ° S’) P(Ec’|S’)P(S’) = P(Ec’ ° S’) P(Ec’|S)P(S) = P(Ec ’° S) = .27 = .63 = .08 = .02 23 . 27 . 08 . 08 . ) ' ( ) ' | ' ( ) ( ) | ' ( ) ( ) | ' ( ) ' | ( = + = + = S P S E P S P S E P S P S E P E S P c c c c
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1/5/10 Example 2 Answer the following questions: a) Two days before, what is your estimate of the probability of the surprise party? Answer: Since you have not yet “read her eyes” the day before the party, you must go on past data and guess that the chances are 10% b) The day before, she does not make ) ' ( ) ' | ' ( ) ( ) | ' ( ) ( ) | ' ( ) ' ( ) ( ) | ' ( ) ' | ( S P S E P S P S E P S P S E P E P S P S E P E S P c c c c c c + = =
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1/5/10 Bayes Theorem P(Ec |S) = P(Ec p S)/P(S) P(S |Ec) = P(S ° Ec)/P(Ec)
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1/5/10 Bayes Theorem P(Ec |S) = P(Ec p S)/P(S) P(S |Ec) = P(S ° Ec)/P(Ec) Therefor e P(Ec S S) = P(Ec | S)*P(S) P(S ± Ec) = P(S | Ec)*P(Ec)
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1/5/10 Bayes Theorem P(Ec |S) = P(Ec p S)/P(S) P(S |Ec) = P(S ° Ec)/P(Ec) Therefor e P(Ec S S) = P(Ec | S)*P(S) P(S ± Ec) = P(S | Ec)*P(Ec) Therefor e P(Ec ( S) = P(S m Ec) P(Ec |S)*P(S) = P(S | Ec)*P(Ec)
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