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March 10th, 2011, 02:59 PM   #1
Joined: Feb 2009

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bayes theorem question

You are serious student who studies on Friday nights but your roommate goes out and has a good time. 40% of the time he goes out with his girlfriend; 60% of the time he goes to a bar. 30% of the times when he goes out with his girlfriend he spends the night at her apartment. 40% of the times when he goes to a bar he gets in a fight and gets thrown in jail. You wake up on saturday morning and your roommate is not home. What is the probability that he is in jail?

Attempt :

A = Not Home
B = In Jail

p(B|A) = P(B n A )/ P(A)

P(A) = 0.4*0.3 + 0.6 * 0.4 =0.36
P(B n A) = (0.6)(0.4) = 0.24

Thus P(B|A) = 0.24 / 0.36 = 2/3

Is that correct?
tnutty is offline  
March 11th, 2011, 07:30 AM   #2
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From: Lexington, MA

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Re: bayes theorem question

Hello, tnutty!

Absolutely correct! . . . Good work!

soroban is offline  
March 17th, 2011, 01:52 AM   #3
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Re: bayes theorem question


I need to calculate certain probability but there is also multivariate probability that I am using. Is this formula correct?

P(something) = P(ST) * P(IP?ST) * P(OP?(IP?ST)) = P(ST) * P(IP?ST) * (P(ST?IP?OP))/(P(IP?ST)) = P(ST) * P(IP?ST) * (P(ST?IP?OP))/(P(IP?ST)*P(ST)) = P(ST?IP?OP)
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