Addition and Multiplication Rules

The addition rule and multiplication rule give two very useful, practical techniques for finding probabilities.

The addition rule applies when we are interested in several outcomes, at most one of which can occur. We add the individual probabilities to get the total.

The multiplication rule applies when we want several things to happen in sequence, and the probability of each successive thing is not affected by earlier outcomes. Here we multiply at each step.

Sometimes we use both rules at once by splitting a complex event into cases, find the probability of each by multiplying, and add to get the total.