# What is the addition rule for mutually exclusive events?

Jan 9, 2015

If events A and B are mutually exclusive of each other, then: $P \left(A \mathmr{and} B\right) = P \left(A\right) + P \left(B\right)$

Mutually exclusive means that A and B cannot occur at the same time, which means P(A and B) = 0.

For example, with a single six-sided die, the probability that you roll a "4" in a single roll is mutually exclusive of rolling a "6" on that same roll because a single die can only show 1 number at a time.

In this example, if event A is rolling a "6" and event B is rolling a "4", then P(A) = 1/6 and P(B) = 1/6, and the addition rule for these two mutually exclusive events is:

$\frac{1}{6} + \frac{1}{6} = \frac{1}{3}$

Thus, the addition of these two events equals $\frac{1}{3}$.