# Homework day 1 pg 440 6 65 68 70 pg 454 6 86 88 day 2

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Homework: Day 1: pg 440 6-65, 68, 70 pg 454 6-86, 88 Day 2: 6.72, 73, 76, 81, 82, 94

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Chapter 6: Probability and Simulation: The Study of Randomness Chapter 6: Review Objectives: Students will be able to: Summarize the chapter Define the vocabulary used Know and be able to discuss all sectional knowledge objectives Complete all sectional construction objectives Successfully answer any of the review exercises Vocabulary: None new Probability Rules 0 ≤ P(X) ≤ 1 for any event X P(S) = 1 for the sample space S Addition Rule for Disjoint Events: P(A B) = P(A) + P(B) Complement Rule: For any event A, P(A C ) = 1 – P(A) Multiplication Rule: If A and B are independent, then P(A B) = P(A) × P(B) General Addition Rule (for nondisjoint) Events: P(E F) = P(E) + P(F) – P(E F) General Multiplication rule: P(A B) = P(A) × P(B | A) Probability Terms Disjoint Events: P(A B) = 0 Events do not share any common outcomes Independent Events: P(A B) = P(A) × P(B) (Rule for Independent events) P(A B) = P(A) × P(B | A) (General rule) P(B) = P(B|A) (lines 1 and 2 implications) Probability of B does not change knowing A At Least One: P(at least one) = 1 – P(none) From the complement rule [ P(A C ) = 1 – P(A) ] Impossibility: P(E) = 0 Certainty: P(E) = 1 Homework: pg 459 – 60; 6-98, 99, 101-106 Problem 1a: At a recent movie, 1000 patrons (560 females and 440 males) were asked whether or not they liked the film. In was determined that 355 females liked the film and 250 males said they enjoyed it also. If a person is randomly selected from the moviegoers what is the probability that the moviegoers was: a) male? b) a female and liked the film c) a male or someone who disliked the film? d) a male and disliked the film? e) a male given they liked the film? f) someone who liked the film given they were a female? g) Are sex and film preference independent? Problem 1b: If P(A) = .3 and P(B) = .45 and events A and B are mutually exclusive find P(A or B).
Chapter 6: Probability and Simulation: The Study of Randomness Problem 1c: When spot-checked for safety, automobiles are found to defective tires 15% of the time, defective lights 25% of the time, and both defective tires and lights 8% of the time. Find the probability that a randomly chosen car has defective lights given that its tires are found to be defective. Problem 2: Elaine is enrolled in a self-paced course that allows three attempts to pass an exam on the material. She does not study and has probability 0.2 of passing on the first try. If she fails on the first try, her probability of passing on the second try increases to 0.3 because she learned something on the first attempt. If she fails on two attempts, the probability of passing on a third attempt is 0.4. She will stop as soon as she passes. The course rules force her to stop after three attempts in any case. Draw a tree diagram to illustrate what is described above, and use it to determine the probability that Elaine passes the exam.

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