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Chapter4.5

# Chapter4.5 - 4.5 General Probability Rules Rules of...

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4.5 General Probability Rules Rules of Probability Rule 1 . 1 ) ( 0 A P for any event A Rule 2 . 1 ) ( = S P Rule 3 . Complement rule: For any event A, ) ( 1 ) ( A P A P c - = Rule 4 . Addition rule: If A and B are disjoint events, then A P ( or ) ( ) ( ) B P A P B + = Rule 5 . Multiplication rule: If A and B are independent events, then A P ( and ) ( ) ( ) B P A P B = Union The union of any collection of events is the event that at least one of the collection occurs.

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Figure 4.15 The addition rule for disjoint events: P(A or B or C)=P(A)+P(B)+P(C) when events A, B, and C are disjoint. Addition Rule for Disjoint Events If events A, B, and C are disjoint in the sense that no two have any outcomes in common, then ( P one or more of ) ( ) ( ) ( ) , , C P B P A P C B A + + = This rule extends to any number of disjoint events.
Figure 4.17 The general addition rule: P(A or B)=P(A)+P(B)-P(A and B) for any events A and B. General Addition Rule for Unions of Two events For any two events A and B, A P ( or A P B P A P B ( ) ( ) ( ) - + = and ) B

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4.18 Venn diagram and probabilities for Example 4.30. Example 4.3 0 Deborah and Matthew are anxiously awaiting word on whether they have been made partners of their law firm. Deborah guesses that her probability of making partner is 0.7 and that Matthew’s is 0.5. P(at least one is promoted)=0.7+0.5-0.3=0.9
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Chapter4.5 - 4.5 General Probability Rules Rules of...

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