5.3 Independence and the Multiplication Rule

Computing Probabilities of Independent Events

1) Use classical method if outcomes are equally likely 2) Use Multiplication Rule for Independent Events.

Multiplication Rule for Independent Events

If E and F are independent events, then: P(E and F) = P(E) x P(F) Can be used for 3 or more Independent Events P(E1 and E2 and E3...En) = P(E1) x P(E2) x ...P(En))

Independent and Dependent Events

Independent events - occurrence of Event *E* in a probability experiment does not affect the probability of Event *F*. Dependent events - occurrence of Event *E* in a probability experiment does affect the probability of Event *F*.

Disjoint Events vs. Independent Events

Two events that are disjoint are not independent. If you know that one event occurs with disjointed Events, then you know the other event did not occur. By its nature, these Events are dependent, therefore cannot be Independent.

Computing "At Least" Probabilities

Use the Compliment Rule