1. Conditional Probability and Independence

2. Learning Targets 1. I can calculate conditional probability using a 2-way table. 2. I can determine whether 2 events are independent. 3. I can use a tree diagram to describe chance behavior. 4. I can use the general multiplication rule to solve probability questions.

3. Conditional Probability The probability that one event happens given that another event is already known to have happened is called a conditional probability. Suppose we know that event A has happened. Then the probability that event B happens given that event A has happened is denoted by P(B A).

4. Card Problem Define event A as a heart and event B as a face card. 1.Find P(A B) 2.Find P(B A)

5. Independent Events Suppose you toss a fair coin twice. Define events A: first toss is a head, and B: second toss is a head. 1.Make a sample space. 2.Find P(A) 3.Find P(A | B) 4.Find P(B) 5.Find P(B | A) Two events A and B are independent if the occurrence of one event has no effect on the chance that the other event will happen. In other words events a and B are independent if P(A | B) = P(A) and P(B | A) = P(B).

6. Tree Diagram A.Draw a tree diagram that shows the sample space for this chance process. B.Find the probability that both students suffer from allergies.

7. General Multiplication Rule