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NotesAug27

# NotesAug27 - More on prevention of double counting(or...

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More on prevention of double counting (or Inclusion-Exclusion Formula) P ( A 1 A 2 A 3 ) = P ( A 1 ) + P ( A 2 ) + P ( A 3 ) - P ( A 1 A 2 ) - P ( A 1 A 3 ) - P ( A 2 A 3 ) + P ( A 1 A 2 A 3 ) .

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Example The three major options on a cer- tain type of a new car are 6-speed transmis- sion (Option I), a power sunroof (Option II) and DVD navigation with GPS (Option III). If of all purchasers 70% request Option I 80% request Option II 75% request Option III 65% request Options I and II 55% request Options I and III 60% request Options II and III 50% request Options I, II and III what is the proportion of all purchasers that request at least one of the options?
Checking that the inclusion-exclusion for- mula does the right thing

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Conditional probability Recall that, if A and B are two events then the conditional probability of A given B is denoted by P ( A | B ) and defined by P ( A | B ) = P ( A B ) P ( B ) , provided P ( B ) > 0. If P ( B ) = 0, then the conditional probability of A given B is not defined
Multiplication rule Directly from the definition of conditional prob- ability P ( A B ) = P ( B ) P ( A | B ) .

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NotesAug27 - More on prevention of double counting(or...

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