Tree Diagrams

 A tree diagram helps us think through conditional probabilities by showing sequences of events as paths that look like branches of a tree.  Making a tree diagram for situations with conditional probabilities is consistent with our “make a picture” mantra.

 The first branch of our tree separates people according to their drinking habits. We label each branch of the tree with a possible outcome and it’s corresponding probability.  What do all the probabilities add up to?

 Because the probability of having an alcohol-related accident depends on one’s drinking behavior. Because the probabilities are conditional, we draw the alternatives separately on each branch of the tree.

 What’s the probability of getting in an accident?  What’s the probability of not getting into an accident?  What’s the probability of getting into an accident given that the alcohol consumption was moderate?