L11-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 11 General Probability Rules Lecture 11 1 Review

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5/25/11 Lecture 11 1 STOR 155 Introductory Statistics Lecture 11: General Probability Rules The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
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5/25/11 Lecture 11 2 Review • Outcome, Sample space, Event • Union ( or ), Intersection ( and ), Complement, Disjoint, … • Venn diagram • Basic rules: – For any event A , P ( not A ) = 1 - P ( A ). – If A and B are disjoint, then P ( A B ) = 0. – For any two events A and B , P ( A B ) = P ( A ) + P ( B ) - P ( A B ).
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5/25/11 Lecture 11 3 General Addition Rule
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5/25/11 Lecture 11 4 Independence A and B are independent if knowing that one occurs does not change the probability that the other occurs. • For independent events A and B , P ( A B ) = P ( A ) P ( B ) ( Multiplication rule )
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5/25/11 Lecture 11 5 Cards ( Ex 1 ) A card is drawn from a deck of 52 playing cards. What is the probability that the card is -- a club? (event A ) -- a king? (event B ) -- a club and a king? (event A B ) Are A and B independent?
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5/25/11 Lecture 11 6 Independent vs Disjoint A and B are independent if and only if P ( A B ) = P ( A ) P ( B ) • If A and B are disjoint, P ( A B) = 0 • Note : If P ( A ) > 0 and P ( B ) > 0, then disjoint A , B are dependent . ( A happens simply implies that B does not happen!)
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5/25/11 7 • The probability of an event measures how likely it will occur. • A conditional probability predicts how likely an event will occur under specified conditions . P ( A | B ) = the conditional probability that A occurs ( uncertain ), given that B has occurred ( certain ).
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This note was uploaded on 11/18/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Summer '08 term at UNC.

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L11-ss - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics Lecture 11 General Probability Rules Lecture 11 1 Review

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