Mutually exclusive events

Property If $A$ and $B$ are mutually exclusive events, then $$ \operatorname{P}(A \text{ or } B) = \operatorname{P}(A) + \operatorname{P}(B) $$.

Explanation Think about flipping a single coin—you can get heads, or you can get tails, but you can't possibly get both at the very same time. These types of events are 'mutually exclusive' because they can never happen together. Calculating the probability of one OR the other happening is super easy: you just add their individual probabilities together!

Examples What is the probability of rolling a sum of 6 or a sum of 11 with two dice? $\operatorname{P}(6 \text{ or } 11) = \operatorname{P}(6) + \operatorname{P}(11) = \frac{5}{36} + \frac{2}{36} = \frac{7}{36}$. From a deck of cards, what's the chance of drawing a 7 or a Jack? $\operatorname{P}(7 \text{ or Jack}) = \operatorname{P}(7) + \operatorname{P}(\text{Jack}) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13}$. A weather forecast gives a 30% chance of only rain and a 25% chance of only snow. What is the chance of rain or snow? $\operatorname{P}(\text{rain or snow}) = 0.30 + 0.25 = 0.55$.