1. Introductory Statistics Lesson 3.2 B Objectives: SSBAT use the multiplication rule to find the probability of 2 events occurring in sequence. SSBAT use the multiplication rule to find conditional probabilities.

2. Review. Independent Events  The probability of the 1 st event does NOT affect the probability of the 2 nd event. Dependent Events  The 1 st event affects the probability of the 2 nd event.

3. Multiplication Rule  Used to find the probability of 2 events, A and B, occurring in sequence  There are 2 cases: - A and B are Independent Events - A and B are Dependent Events Multiplication Rule and Independent Events If A and B are Independent events then P(A and B) = P(A) ∙ P(B)

7. 4.The probability that a particular knee surgery is successful is 0.85. Find the probability that 2 knee surgeries are successful. P(success and success) = P(S) · P(S) P(S and S) = (0.85)(0.85) P(S and S) = 0.7225

8. 5.The probability that a particular knee surgery is successful is 0.85. Find the probability that both surgeries are not successful.  Probability of Not Successful is 1 – 0.85 = 0.15 P(Not and Not) = P(Not) · P(Not) P(Not and Not) = (0.15)(0.15) P(Not and Not) = 0.0225

9. 6.The probability that a particular knee surgery is successful is 0.85. Find the probability that the first one is successful and the second one is not successful. P(Success and Not) = P(Success) · P(Not) P(Success and Not) = (0.85)(0.15) P(Success and Not) = 0.1275

10. Multiplication Rule and Dependent events If A and B are Dependent events then P(A and B) = P(A) ∙ P(B|A)

12.  Complete Worksheet 3.2 B