lec2.2 - 38 Lecture 4: CHAPTER 2: PROBABILITY Counting...

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38 Lecture 4: CHAPTER 2: PROBABILITY Counting Methods (Section 2.2, page 62) Permutations: In how many ways can you order the letters A, B, C? Five lifeguards are available for duty one Saturday afternoon. There are three lifeguard stations. In how many ways can three lifeguards be chosen and ordered among the stations?
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39 Combinations: Let’s look at the lifeguard question again. If I denote the 5 people as A, B, C, D, E, how do I get 60 permutations? At a certain event, 30 people attend, and 5 will be chosen at random to receive door prizes. The prizes are all the same, so the order in which the people are chosen does not matter. How many different groups of five people can be chosen?
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40 Conditional Probability and Independence (Section 2.3, page 69) Conditional Probability The term conditional probability comes from the fact that sometimes, the probability that A occurs depends heavily on whether B has occurred. At other times, when the occurrence or nonoccurrence of B has no effect whatsoever on the probability that A occurs, we say that A and B are independent events . Definition: Example (revisited): In a process that manufactures aluminum cans, the probability that a can has a flaw on its side is 0.02, the probability that a can has a flaw on the top is 0.03, and the probability that a can has a flaw on both the side and the top is 0.01. (a) What is the probability that a can will have a flaw on the side, given that is has a flaw on top? Let A and B be two events with 0 ) ( B P . The conditional probability of A occurring given that B has already occurred is denoted by ) | ( B A P and can be calculated from the formula: ) ( ) ( ) ( ) ( ) | ( B P B A P B P AandB P B A P Similarly, Let A and B be two events with 0 ) ( A P . The conditional probability of B occurring given that A has already occurred is denoted by ) | ( A B P and can be calculated from the formula: ) ( ) ( ) ( ) ( ) | ( A P B A P A P AandB P A B P
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41 (b) What is the probability that a can will have a flaw on the top, given that it has a flaw on the side? Note: This definition implies that for any events A and B ) ( ) | ( ) ( ) | ( ) ( A P A B P B P B A P B A P This statement is called the Multiplication Rule. Example:
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This note was uploaded on 06/20/2011 for the course STAT 2800 taught by Professor Paula during the Winter '11 term at UOIT.

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lec2.2 - 38 Lecture 4: CHAPTER 2: PROBABILITY Counting...

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