sta4321-3 - If AB = , then P ( A B ) = P ( A ) + P ( B ) ....

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§2.4 Counting Rules Useful in Probability
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From Last Time Algebraic Laws Let S be a sample space and A , B , C be three events in S . Cumulative Law A B = B A AB = BA Associative Law ( A B ) C = A ( B C ) ( AB ) C = A ( BC ) Distributive Law A ( B C )= AB AC A ( BC )=( A B )( A C ) De Morgan’s Laws ± n i = 1 A i = ² n i = 1 A i ² n i = 1 A i = ± n i = 1 A i Arthur Berg §2.4 Counting Rules Useful in Probability 2/ 4
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From Last Time Defnition o± a Probability Defnition (probability) A probability is a mapping o± events to the real numbers such that the ±ollowing three conditions hold: (i) P ( A ) 0 ±or any event A ; (ii) P ( S )= 1 where S is the sample space; (iii) A 1 , A 2 , . . . are mutually exclusive (meaning A i A j = ±or any i ± = j ) then P ± ² i = 1 A i ³ = ´ i = 1 P ( A i ) . Arthur Berg §2.4 Counting Rules Use±ul in Probability 3/ 4
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From Last Time Implications of conditions (i)-(iii) (a) P ( )= 0. (b)
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Unformatted text preview: If AB = , then P ( A B ) = P ( A ) + P ( B ) . (c) For any events A and B , P ( A B ) = P ( A ) + P ( B )-P ( AB ) . (d) If A B , then P ( A ) P ( B ) . (e) For any event A , 0 P ( A ) 1. (f) P ( A ) = 1-P ( A ) (g) Principle of Inclusion-Exclusion Theorem (Principle of Inclusion-Exclusion) Given events E 1 , . . . , E n , P ( n i = 1 E i ) = n i = 1 P ( E i )- i 1 < i 2 P ( E i 1 E i 2 ) + + (-1 ) r + 1 i 1 < i 2 < ir P ( E i 1 E i 2 E ir ) + + (-1 ) n + 1 P ( E 1 E n ) Arthur Berg 2.4 Counting Rules Useful in Probability 4/ 4...
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This note was uploaded on 10/04/2011 for the course STA 4321 taught by Professor Staff during the Fall '08 term at University of Florida.

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sta4321-3 - If AB = , then P ( A B ) = P ( A ) + P ( B ) ....

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