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A denotes event that present was hidden by mom. B denotes event that present was hidden by dad. E denotes event that present was hidden upstairs. F denotes event that present was hidden downstairs.

P(A)=.6 P(B)=.4 P(E|A)=.7 P(F|A).3 P(E|B)=.5 P(F|B)=.5

Find P(E)

Can you explain why the answer is: P(E) = P(A)P(E|A)+P(B)P(E|B) = (.6)(.7)+(.4)(.5) = .42 +.2 = .62

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    What do you think the probability is that mom hid the present upstairs? And the probability that dad hid the present upstairs?2012-09-18

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The present could be upstairs in two different (and disjoint) ways: (i) Mom hid the hiding and hid the present upstairs or (ii) Dad did the hiding and hid it upstairs.

What is the probability of (i)? In symbols, it is $\Pr(A\cap E)$. But we have the general formula $\Pr(X|Y)\Pr(Y)=\Pr(X\cap Y)=\Pr(Y\cap X).$ Putting $X=E$ and $Y=A$ gives us $\Pr(A\cap E)$.

Do a similar calculation for the probability of (ii), that is, $\Pr(B\cap E)$.

Then add up.

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    thank you Andre, i get it now, can you perhaps take a look at this: http://math.stackexchange.com/questions/198697/bayes-theorem-confusion-more-complex it's abit more complex version of the Bayes2012-09-18