# 3.2: Independent and Mutually Exclusive Events

Independent and mutually exclusive do not mean the same thing.

## Independent Events

Two events are independent if one of the following are true:

• Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of two roles of a fair die are independent events. The outcome of the first roll does not change the probability for the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are NOT independent, then we say that they are dependent.

Sampling may be done withreplacement or without replacement.

• If it is not known whether A and B are independent or dependent, assume they are dependent until you can show otherwise.
1. Compute $$P(T)$$.
2. Compute $$P(T|F)$$.
3. Are $$T$$ and $$F$$ independent?.
4. Are $$F$$ and $$S$$ mutually exclusive?
5. Are $$F$$ and $$S$$ independent?