1 / 24

Section 6.3 Probability Models

Section 6.3 Probability Models. Statistics AP Mrs. Skaff. Today you will learn how to…. Construct Venn Diagrams, Tables, and Tree Diagrams and use them to calculate probabilities Calculate probabilities for nondisjoint events

liko
Download Presentation

Section 6.3 Probability Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 6.3Probability Models Statistics AP Mrs. Skaff

  2. Today you will learn how to… Construct Venn Diagrams, Tables, and Tree Diagrams and use them to calculate probabilities Calculate probabilities for nondisjoint events Modify the multiplication rule to accommodate non-independent events Calculate conditional probabilities AP Statistics, Section 6.3, Part 1

  3. Non-Independent Events You draw a card from a deck and then draw another one without replacing the first card. What is the probability that you draw a red card and then a diamond? AP Statistics, Section 6.3, Part 1

  4. GENERAL MULTIPLICATION RULE The joint probability that both of two events A and B happen together can be found by P(A and B) = P(A)P(B|A) Here P(B|A) is the conditional probability that B occurs given the information that A occurs.

  5. Venn Diagrams: Disjoint Events S A B

  6. Venn Diagrams: Disjoint Events Rule #3 (addition rule for disjoint events!) P(A or B) = P(A) + P(B) S A B

  7. Venn Diagrams: Non-disjoint Events P(A or B) = P(A) + P(B) – P(A and B) S B A A and B

  8. Venn Diagrams: Non-disjoint Events S A B A and B

  9. Example • Lindsey and Clint are awaiting the decision about a promotion. Lindsey guesses her probability of her getting a promotion at .7 and Clint’s probability at .5. Lindsey also thinks the probability of both getting promoted is .3

  10. Example • What’s the probability of either Lindsey or Clint getting promotedP(L or C)? • P(L and Cc)? L C L and C • P(C and Lc)? • P(Lc and Cc)?

  11. A=is young (between 18 and 29) • P(A)=

  12. B=married • P(B)=

  13. A=is young (between 18 and 29) • B=married • P(A and B)=

  14. A=is young (between 18 and 29) • B=married • P(A | B)= (Read as “the probability of A given B”) • This is known as a “conditional probability”

  15. Conditional Probabilities • Conditional probability measures the probability of an event A occurring given that B has already occurred. There is a formula for this in your packets. Sometimes it can be confusing for solving real-life problems… • It is usually easier to use a tree diagram, venn diagram, or table to solve these problems!!! AP Statistics, Section 6.3, Part 1

  16. Conditional Probabilities and Tables • Bag A contains 5 blue and 4 green marbles. Bag B contains 3 yellow, 4 blue, and 2 green marbles. Given you have a green marble, what is the probability it came from Bag A? AP Statistics, Section 6.3, Part 1

  17. Conditional Probabilities and Venn Diagrams • What is the probability of Lindsey being promoted given that Clint got promoted? L C L and C

  18. Probabilities with Tree Diagrams • Example: A videocassette recorder (VCR) manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose 3% of the output from F1 are defective, while only 2% of the output from F2 are defective. What is the probability the part is defective? • Example: A videocassette recorder (VCR) manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose 3% of the output from F1 are defective, while only 2% of the output from F2 are defective. What is the probability the part is defective? • Example: A videocassette recorder (VCR) manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose 3% of the output from F1 are defective, while only 2% of the output from F2 are defective. What is the probability the part is defective? • Example: A videocassette recorder (VCR) manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose 3% of the output from F1 are defective, while only 2% of the output from F2 are defective. What is the probability the part is defective? 0.97 0.679 G F1 Good F1 D F1 Defective 0.021 0.7 0.03 0.3 0.98 0.294 G F2 Good F2 D 0.006 F2 Defective 0.02 Example: A videocassette recorder (VCR) manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose 3% of the output from F1 are defective, while only 2% of the output from F2 are defective. What is the probability the part is defective?

  19. 0.97 0.679 G F1 Good F1 D F1 Defective 0.021 0.7 0.03 0.3 0.98 0.294 G F2 Good F2 D 0.006 F2 Defective 0.02 If a randomly chosen part is defective, what is the probability that it came from factory F1?

  20. Summary…You should be able to: • Construct a Venn Diagram and use it to calculate probabilities • Particularly useful for nondisjoint events • Fill in a table of probabilities and use it to calculate probabilities • Especially useful for conditional probabilities • Construct a Tree Diagram and use it to calculate probabilities AP Statistics, Section 6.3, Part 1

  21. Summary…Formulas • Multiplication Rule • P(A and B) = P(A)P(B|A) • Conditional Probabilities • P(A | B)= P(A and B) / P(B) Probability of nondisjoint events AP Statistics, Section 6.3, Part 1

  22. Coming up…

  23. Assignment • Exercises: 6.66-6.68, 6.70, 6.78, 6.87-6.89, 6.93, 6.95

More Related