## Question 771:

1## Answer:

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The easiest way to answer these conditional probability questions is to use a tree-diagram and multiply out the probabilities on each branch. I've attached a diagram in the file.To use Bayes Theorem on this we first need to know the probability of a garage getting broken into. To do that we just add up the two possible ways this can happen, either with the doors open or not: The probability of getting stolen is .75*.01 + .25*.05 = .0075+.0125 = .02. Now we use this in the Bayes Formula: The probability of the doors left open, given a garage is robbed is :

P(Open) * P(Robbed | Open) / P(Robbed) = (.25 * .05) / .02 = .625 probability doors were left open.