1. Copyright © 2011 Pearson, Inc. 9.3 Probability

2. Copyright © 2011 Pearson, Inc. Slide 9.3 - 2 What you’ll learn about Sample Spaces and Probability Functions Determining Probabilities Venn Diagrams and Tree Diagrams Conditional Probability Binomial Distributions … and why Everyone should know how mathematical the “laws of chance” really are.

3. Copyright © 2011 Pearson, Inc. Slide 9.3 - 3 Probability of an Event (Equally Likely Outcomes)

4. Copyright © 2011 Pearson, Inc. Slide 9.3 - 4 Probability Distribution for the Sum of Two Fair Dice OutcomeProbability 21/36 32/36 43/36 54/36 65/36 76/36 85/36 94/36 103/36 112/36 121/36

5. Copyright © 2011 Pearson, Inc. Slide 9.3 - 5 Example Rolling the Dice Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

6. Copyright © 2011 Pearson, Inc. Slide 9.3 - 6 Example Rolling the Dice Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

7. Copyright © 2011 Pearson, Inc. Slide 9.3 - 7 Probability Function

8. Copyright © 2011 Pearson, Inc. Slide 9.3 - 8 Probability of an Event (Outcomes not Equally Likely)

9. Copyright © 2011 Pearson, Inc. Slide 9.3 - 9 Strategy for Determining Probabilities

10. Copyright © 2011 Pearson, Inc. Slide 9.3 - 10 Strategy for Determining Probabilities

11. Copyright © 2011 Pearson, Inc. Slide 9.3 - 11 Example Choosing Chocolates Dylan opens a box of a dozen chocolate cremes and offers three of them to Russell. Russell likes vanilla cremes the best, but all the chocolates look alike on the outside. If five of the twelve cremes are vanilla, what is the probability that all of Russell’s picks are vanilla?

12. Copyright © 2011 Pearson, Inc. Slide 9.3 - 12 Example Choosing Chocolates If five of the twelve cremes are vanilla, what is the probability that all of Russell’s 3 picks are vanilla?

13. Copyright © 2011 Pearson, Inc. Slide 9.3 - 13 Multiplication Principle of Probability Suppose an event A has probability p 1 and an event B has probability p 2 under the assumption that A occurs. Then the probability that both A and B occur is p 1 p 2.

14. Copyright © 2011 Pearson, Inc. Slide 9.3 - 14 Example Choosing Chocolates Dylan opens a box of a dozen chocolate cremes and offers three of them to Russell. Russell likes vanilla cremes the best, but all the chocolates look alike on the outside. If five of the twelve cremes are vanilla, what is the probability that all of Russell’s picks are vanilla?

15. Copyright © 2011 Pearson, Inc. Slide 9.3 - 15 Example Choosing Chocolates

16. Copyright © 2011 Pearson, Inc. Slide 9.3 - 16 Conditional Probability Formula

17. Copyright © 2011 Pearson, Inc. Slide 9.3 - 17 Binomial Distribution

18. Copyright © 2011 Pearson, Inc. Slide 9.3 - 18 Binomial Distribution  

19. Copyright © 2011 Pearson, Inc. Slide 9.3 - 19 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes all 15?

20. Copyright © 2011 Pearson, Inc. Slide 9.3 - 20 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes all 15?

21. Copyright © 2011 Pearson, Inc. Slide 9.3 - 21 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes exactly 10?

22. Copyright © 2011 Pearson, Inc. Slide 9.3 - 22 Example Shooting Free Throws Suppose Tommy makes 92% of his free throws. If he shoots 15 free throws, and if his chance of making each one is independent of the other shots, what is the probability that he makes exactly 10?

23. Copyright © 2011 Pearson, Inc. Slide 9.3 - 23 Quick Review Solutions