## 13.4 Outline

- Keno games
- Independent events
- independent
- dependent

- Probability of an intersection
- multiplication property of probability
- birthday problem

- Probability of a union
- addition property of probability
- probability of independent events

- Drawing with and without replacement
- Stochastic processes and tree diagrams

## 13.4 Essential Ideas

**Multiplication Property of Probability: **If events *E* and *F* are independent events, then we can find the probability of an intersection by

*P*(*E and F *) = *P*(*E *) times *P*(*F *)

**Addition Property of Probability: **For any events *E* and *F*, the probability of their union can be found by

*P*(*E or F *) = *P*(*E *) + *P*(*F *) − *P*(*E and F *)

Drawing **with replacement** means choosing the first item, noting the result, and then replacing the item back into the sample space before selecting the second item.

Drawing **without replacement** means selecting the first item, noting the result, than then selecting a second item *without* replacing the first item.