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Probability

Precalculus. Lesson 9.3. Probability. Quick Review. 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

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Probability

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  1. Precalculus Lesson 9.3 Probability

  2. Quick Review

  3. 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.

  4. Probability of an Event (Equally Likely Outcomes)

  5. Probability Distribution for the Sum of Two Fair Dice Outcome Probability 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36

  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. 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?

  11. 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.

  12. 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?

  13. Conditional Probability Formula

  14. Binomial Distribution

  15. 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?

  16. 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?

  17. Homework: Text pg728/729 Exercises # 2-8 even, 12-24 (intervals of 4)

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