1.10 Independence

The book provides a (characteristically) terse statement of what it means for two events to be independent of one another.

Definition 1.3 Independence of Events Events \(A, B \in S\) are independent if \[P(A \cap B) = P(A)P(B)\].

In your own words:

• What does it mean for two events to be independent of one another?
• How do you know if two events are independent of one another?
• How do you test if two events are independent of one another?

Try using this idea of independent in two places:

1. Suppose that you are creating a model to predict an outcome. Further, suppose that two events \(A\) and \(B\) are independent of one another. Can you use \(B\) to predict \(A\)?
2. If two events, \(A\) and \(B\) are independent, then what happens if you work through a statement of conditional probability, \(P(A|B)\)?