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.

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

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

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

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.

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

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

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

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.

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?

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?

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

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 = = =

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

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.

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

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?

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

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.

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.

Holt Geometry 3-1 Lines and Angles

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

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?

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

Holt Geometry 3-1 Lines and Angles

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%.

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 = = =

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?