Section 9-7 Probability of Multiple Events

Multiple Events When the occurrence of one event affects the probability of a second event the two events are dependent. When the occurrence of one event does not affect the probability of a second event, then the two events are independent. P(A and B) = P(A) x P(B)

Example Suppose you have five books in your book bag. Three are novels, one is a biography, and one is a poetry book. Today you grab one book out of your bag without looking, and return it later. Tomorrow you do the same thing. What is the probability that you grab a novel both days?

Example Suppose you have five books in your book bag. Three are novels, one is a biography, and one is a poetry book. Today you grab one book out of your bag without looking, and return it later. Tomorrow you do the same thing. What is the probability that you grab a novel both days? Answer: 3/5 x 3/5 = 9/25

Finding P(A or B) When two events cannot happen at the same time, the events are mutually exclusive. Rolling a 5 and rolling a number less than 3 on a number cube are mutually events, because a number cannot be 5 and less then 3 at the same time. When this happens we can say P(A)+P(B) - mutually exclusive events

Now If A and B are not mutually exclusive events then: P(A or B) = P(A) + P(B) – P(A and B)

Example: We have Find the probability of: P(apple or green)

Example: We have Find the probability of: P(apple or green) Answer: 5/9 +3/9 – 2/9 = 6/9 = 2/3

Look at page 534 #1 #5 #19

Look at page 534 #1 Independent #5 #19

Look at page 534 #1 Independent #5 ¼ x 2/3 = 2/12 = 1/6 #19

Look at page 534 #1 Independent #5 ¼ x 2/3 = 2/12 = 1/6 #19 1/6 + 3/6 – 1/6 = 3/6 = ½

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