1. Holt Geometry 3-1 Lines and Angles S-CP.A.2Understand that 2 events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. S-CP.A.5Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. S-CP.B.7Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

2. Holt Geometry 3-1 Lines and Angles  Combined variation  Inverse variation  Joint variation

3. Holt Geometry 3-1 Lines and Angles  Paper for notes  Pearson 11.3  Graphing Calc.

4. Holt Geometry 3-1 Lines and Angles  Notes 11.3  Calculator

5. Holt Geometry 3-1 Lines and Angles TOPIC: 11.3 Probability of Multiple Events Name: Daisy Basset Date : Period: Subject: Notes Objective: Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.

6. Holt Geometry 3-1 Lines and Angles Vocabulary  Dependent events  Independent events  Mutually exclusive events Key Concept  Probability of A and B  Probability of A or B

7. Holt Geometry 3-1 Lines and Angles 1. Are the outcomes of the trial dependent or independent events?

8. Holt Geometry 3-1 Lines and Angles A. Roll a number cube. Then spin a spinner. The events _____ ______ each other. They are _________. independent affect do not

9. Holt Geometry 3-1 Lines and Angles B. Pick one flash card, then another from a stack of 30 flash cards. They are _________.dependent Picking the first card affects the possible outcomes of picking the second card.

10. Holt Geometry 3-1 Lines and Angles 2. At a picnic there are 10 diet drinks and 5 regular drinks. There are also 8 bags of fat-free chips and 12 bags of regular chips?

11. Holt Geometry 3-1 Lines and Angles If you grab a drink and a bag of chips without looking, what is the probability that you get a diet drink and fat-free chips?

12. Holt Geometry 3-1 Lines and Angles Event A = picking a diet drink Event B = picking fat-free chips A and B are __________. Picking a drink has no effect on picking the chips. independent

13. Holt Geometry 3-1 Lines and Angles P(A and B) = P(A) P(B) # of diet drinks total # drinks # of fat-free chip bags total # of bags of chips = = 10 15 8 20 =

14. Holt Geometry 3-1 Lines and Angles 3. You roll a standard die. Are the events mutually exclusive? Explain.

15. Holt Geometry 3-1 Lines and Angles A. Rolling a 2 and a 3 The events are _______________. mutually exclusive You can not roll a 2 and a 3 at the same time.

16. Holt Geometry 3-1 Lines and Angles B. Rolling an even # and a multiple of 3 The events are ___ _______________. mutually exclusive You can roll a 6 – an even # and a multiple of 3 – at the same time. not

17. Holt Geometry 3-1 Lines and Angles SummaryIn your own words, 1. What is the difference between independent and dependent events? 2. What is the difference between independent and mutually exclusive events?

18. Holt Geometry 3-1 Lines and Angles  Notes 11.3  Calculator

19. Holt Geometry 3-1 Lines and Angles 4. At a high school, a student can take 1 foreign language each term. About 37% of the students take Spanish. About 15% of the students take French.

20. Holt Geometry 3-1 Lines and Angles What is the probability that a student chosen at random is taking Spanish or French? One foreign language each term means a student cannot take both at the same time. The events are mutually exclusive.

21. Holt Geometry 3-1 Lines and Angles

22. Holt Geometry 3-1 Lines and Angles P(A or B) = P(A) + P(B) P(Spanish or French) = P(Spanish) + P(French) ≈ 0.37 + 0.15 ≈ 0.52 The probability that a student chosen at random is taking Spanish or French is about 0.52, or about 52%.

23. Holt Geometry 3-1 Lines and Angles 5. Suppose you reach into a dish and select a token at random. What is the probability that the token is round or green?

24. Holt Geometry 3-1 Lines and Angles Are the events mutually exclusive? No; it is possible to have a round AND green token.

25. Holt Geometry 3-1 Lines and Angles

26. Holt Geometry 3-1 Lines and Angles P(A or B) = P(A) + P(B) - P(A and B) P(Round or Green) = P(R) + P(G) - P(R or G) The probability selecting a round or green token is about 0.67, or about 67%.

27. Holt Geometry 3-1 Lines and Angles P(A and B) = P(A) P(B) # of diet drinks total # drinks # of fat-free chip bags total # of bags of chips = = 10 15 8 20 =

28. Holt Geometry 3-1 Lines and Angles SummarySummarize/reflect D What did I do? L What did I learn? I What did I find most interesting? Q What questions do I still have? What do I need clarified?