Stats 309 6-3 & 6-5_1

Stats 309 6-3 & 6-5_1 - 6.3 Probability Rules and Trees...

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Unformatted text preview: 6.3 Probability Rules and Trees Complement Rule P(A) + P(A c ) = 1 P(A) = 1 P(A c ) Addition Rule: P(A B) = P(A) + P(B) P(A B) If A and B are mutually exclusive, then P(A B) = 0. So P(A B) = P(A) + P(B) for two mutually exclusive events. Conditional Probability: Multiplication Rule: P(A B) = P(A)*P(B|A) = P(B)*P(A|B) If A and B are independent events, then P(A B) = P(A)*P(B) ) ( ) ( ) | ( B P B A P B A P = Example 6.5 page 171 A graduate statistics course has seven male and three female students. The professor wants to select two students at random to help her conduct a research project. What is the probability that the two students chosen are female? Let A represent the event that the first student chosen is female and B represent the event that the second student chosen is also female. The problem is that event B depends on what happens with event A. We are looking for P(A and B). We have: P(A) = 3/10 P(B|A) = 2/9 We can use the multiplication rule P(A and B) = P(B|A)P(A) P(A and B) = 3/10 * 2/9 = .067 Example 6.6 page 172 Suppose the professor is sick and will be out for two classes....
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Stats 309 6-3 & 6-5_1 - 6.3 Probability Rules and Trees...

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