40 Algorithms Every Programmer Should Know

Addition rules for OR events

When calculating the probability of either one event or the other occurring (mutually exclusive), the following simple addition rule is used:

P(outcome 1 OR outcome 2) = P(outcome 1) + P(outcome 2)

For example, what is the probability of rolling a 6 or a 3? To answer this question, first, note that both outcomes cannot occur simultaneously. The probability of rolling a 6 is (1 / 6) and the same can be said for rolling a 3:

P(6 OR 3) = (1 / 6) + (1 / 6) = 0.33 (33%)

If the events are not mutually exclusive and can occur simultaneously, use the following general addition formula, which is always valid in both cases of mutual exclusiveness and of non-mutual exclusiveness:

P(outcome 1 OR outcome 2) = P(outcome 1) ...