# B doesnt stop at either light c must stop just at the

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b) doesn't stop at either light? c) must stop just at the first light? Homework: Day 1: 6-22, 24, 25, 29, 34, 36 Day 2: 6.37, 38, 40, 44, 46, 50, 57

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Chapter 6: Probability and Simulation: The Study of Randomness Section 6.3: General Probability Rules Knowledge Objectives: Students will: Define what is meant by a joint event and joint probability . Explain what is meant by the conditional probability P ( A | B ). State the general multiplication rule for any two events . Explain what is meant by Bayes’s rule . Construction Objectives: Students will be able to: State the addition rule for disjoint events . State the general addition rule for union of two events . Given any two events A and B , compute P ( A B ) . Given two events, compute their joint probability . Use the general multiplication rule to define P ( B | A ). Define independent events in terms of a conditional probability. Vocabulary: Personal Probabilities – reflect someone’s assessment (guess) of chance Joint Event – simultaneous occurrence of two events Joint Probability – probability of a joint event Conditional Probabilities – probability of an event given that another event has occurred Key Concepts: General Addition Rule For any two events E and F, P(E or F) = P(E) + P(F) – P(E and F) E F E and F P(E or F) = P(E) + P(F) – P(E and F) Probability for non-Disjoint Events
Chapter 6: Probability and Simulation: The Study of Randomness General Multiplication Rule The probability that two events A and B both occur is P(A and B) = P(A B) = P(A) ∙ P(B | A) where P(B | A ) is a conditional probability read as the probability of B given that A has occurred Conditional Probability Rule If A and B are any two events, then P(A and B) N(A and B) P(B | A) = ----------------- = ---------------- P(A) N(A) N is the number of outcomes

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Chapter 6: Probability and Simulation: The Study of Randomness Example 1: A construction firm has bid on two different contracts. Let B 1 be the event that the first bid is successful and B 2 , that the second bid is successful. Suppose that P(B 1 ) = .4, P(B 2 ) = .6 and that the bids are independent. What is the probability that: a) both bids are successful? b) neither bid is successful? c) is successful in at least one of the bids? Example 2 : Given that P(A) = .3 , P(B) = .6, and P(B|A) = .4 find: a) P(A and B) b) P(A or B) c) P(A|B) Example 3 : Given P(A | B) = 0.55 and P(A or B) = 0.64 and P(B) = 0.3. Find P(A). Example 4 : If 60% of a department store’s customers are female and 75% of the female customers have a store charge card, what is the probability that a customer selected at random is female and had a store charge card? Example 5: Suppose 5% of a box of 100 light blubs is defective. If a store owner tests two light bulbs from the shipment and will accept the shipment only if both work. What is the probability that the owner rejects the shipment? Example 6 : Dan can hit the bulls eye ½ of the time Daren can hit the bulls eye of the time Duane can hit the bulls eye ¼ of the time Given that someone hits the bulls eye, what is the probability that it is Dan?
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