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Unformatted text preview: If AB = âˆ… , then P ( A âˆª Â· B ) = P ( A ) + P ( B ) . (c) For any events A and B , P ( A âˆª B ) = P ( A ) + P ( B )P ( AB ) . (d) If A âŠ‚ B , then P ( A ) â‰¤ P ( B ) . (e) For any event A , 0 â‰¤ P ( A ) â‰¤ 1. (f) P ( Â¯ A ) = 1P ( A ) (g) Principle of InclusionExclusion Theorem (Principle of InclusionExclusion) Given events E 1 , . . . , E n , P ( âˆª n i = 1 E i ) = n Â± i = 1 P ( E i )Â± i 1 < i 2 P ( E i 1 E i 2 ) + Â· Â· Â· Â· Â· Â· + (1 ) r + 1 Â± i 1 < i 2 < Â·Â·Â· ir P ( E i 1 E i 2 Â· Â· Â· E ir ) + Â· Â· Â· + (1 ) n + 1 P ( E 1 Â· Â· Â· E n ) Arthur Berg Â§2.4 Counting Rules Useful in Probability 4/ 4...
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 Fall '08
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 Addition, Counting, Probability, Elementary algebra, Greatest common divisor, Arthur Berg

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