1. 9.3
Probability

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. Probability of an Event (Equally Likely Outcomes)

4. Probability Distribution for the Sum of Two Fair Dice
Outcome Probability
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5. Example Rolling the Dice
Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

6. Example Rolling the Dice
Find the probability of rolling a sum divisible by 4 on a single roll of two fair dice.

7. Probability Function

8. Probability of an Event (Outcomes not Equally Likely)

9. Strategy for Determining Probabilities

10. Strategy for Determining Probabilities

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. 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. Multiplication Principle of Probability
Suppose an event A has probability p1 and an event B has probability p2 under the assumption that A occurs. Then the probability that both A and B occur is p1p2.

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. Example Choosing Chocolates

16. Conditional Probability Formula

17. Binomial Distribution

18. Binomial Distribution 

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. 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. 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. 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. Quick Review Solutions