Determining Independence of Events: Comparing Conditional and Simple Probabilities

This lesson teaches how to determine if two events, A and B, are independent by comparing the conditional probability of A given B to the simple probability of A. It explains the concept of conditional probability and independence, highlights common misunderstandings, and uses a two-way table example to demonstrate the process. The lesson concludes by confirming that if the probabilities are equal, the events are independent.

What is the conditional probability of A given B?

Explain the difference between the probability of A given B and the probability of B given A.

How can you determine if two events are independent?

What were the simple and conditional probabilities of playing an instrument in Jen's class?

What conclusion can be drawn about playing an instrument and playing a sport in Jen's class?