Handout_4_5_fall11(2 - 4.5 General Probability Rules Previous Probability Rules 1 The probability P(A of any event A satisfies 0 P(A 1 2 All

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4.5 General Probability Rules Previous Probability Rules 1) The probability P( A ) of any event A satisfies 0 P( A ) 1. 2) All possible outcomes together must have probability 1. P( S ) = 1. 3) Two events A and B are disjoint →P( A or B ) = P( A ) + P( B ) 4) The complement rule states that→ P( A c ) = 1 – P( A ) 5) Two events A and B are independent P( A and B ) = P( A )P( B ) General addition rules The union of any collection of events is the event that at least one of the collection occurs. The intersection of any collection of events is the event that all of the events occur. 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 A , B , C ) = P( A ) + P( B ) + P( C ) P (union of A , B , C ) = P( A ) + P( B ) + P( C ) This rule extends to any number of disjoint events.
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For any two events A and B , P( A or B ) = P( A ) + P( B ) – P( A and B ) Example #1 Consider tossing a die once. Let A be the event that you get a 1. Let B be the event that you get an odd number. What is the P( A or B )? Here, A and B are not disjoint. ●before (restrictive rule (4.2), holds only if A and B are disjoint): P( A or B ) = P( A ) + P( B ) ●now (general rule (4.5), holds whether or not A and B are disjoint): P( A or B ) = P( A ) + P( B ) – P( A and B ) Example #2 Consider tossing a die once. Let A be the event that you get a 1.
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This note was uploaded on 02/22/2012 for the course PAM 2100 taught by Professor Abdus,s. during the Fall '08 term at Cornell University (Engineering School).

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Handout_4_5_fall11(2 - 4.5 General Probability Rules Previous Probability Rules 1 The probability P(A of any event A satisfies 0 P(A 1 2 All

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