Addition and Multiplication Rules

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.

Tree Diagrams

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?

Tree Diagrams

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.

Tree Diagrams

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?

Tree Diagrams