Conditional Probability and Independence

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.

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).

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)

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).

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.

General Multiplication Rule