Determining Independence of Events: Comparing Conditional and Simple Probabilities

The video tutorial explains how to determine if two events are independent by comparing the conditional probability of one event given another to the simple probability of the first event. It covers the conditional probability formula, the concept of independence, and provides a practical example using a two-way table. The tutorial concludes by emphasizing that if the probabilities are not equal, the events are associated and not independent.

What is the formula for finding the conditional probability of event A given event B?

• Probability of B divided by probability of A

• Probability of A and B divided by probability of B

• Probability of A divided by probability of B

• Probability of A and B divided by probability of A

How can you determine if two events are independent?

• By checking if the conditional probability of A given B is greater than the simple probability of A

• By checking if the conditional probability of A given B is less than the simple probability of A

• By checking if the conditional probability of A given B is not equal to the simple probability of A

• By checking if the conditional probability of A given B is equal to the simple probability of A

What is a common misunderstanding about associated events?

• Thinking that events are associated when the conditional probability is slightly different from the simple probability

• Thinking that events are independent when the conditional probability is slightly different from the simple probability

• Thinking that events are associated when the probabilities are exactly equal

• Thinking that events are independent when the probabilities are exactly equal

In the example from Jen's class, what was the simple probability of a student being female?

• 59%

• 50%

• 71%

• 65%

What conclusion was drawn about the independence of being female and being a soccer player in Jen's class?

• They are independent because the probabilities are equal

• They are not independent because the probabilities are not equal

• They are not independent because the probabilities are exactly equal

• They are independent because the probabilities are close to equal