Lecture 11

# Lecture 11 - given that event B has already occurred is...

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More Probability The Intersection of two events A and B is the set of all common outcomes of both A and B. The intersection is denoted by I . Ex. Roll a die Let A be the event of an odd number Let B be the event of a number at most 4 A={ B={ What is A I B? What is P(A I B )? S = { A I B = { P(A I B ) = n(A I B )/n(S) =

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The Union of two events A and B is the combination of all outcomes of both A and B. Union is denoted by U . Ex. Roll a die Let A be the event of an even number Let B be the event of a number at least 4 A={ B={ What is A U B? What is P(A U B )? A U B = { P(A U B) = n(A U B)/n(S) = General addition rule P(A U B ) = P(A) + (B) - P(A I B )

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Mutually Exclusive Events Two events A and B are said to be mutually exclusive if and only if A I B = (the empty set, i.e nothing in common)
Conditional Probability The probability that one event occurs given that another event has occurred. Let A and B be events. The probability of event A occurring

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Unformatted text preview: given that event B has already occurred is written as P( A | B ). P(A I B ) P( A | B ) = -------------P( B ) EX. Roll a die What is the probability of getting an odd number given that the number rolled is at most 4? Let A be an odd number and let B be a number at most four. A = { B = { A I B = { P(B) = n(B)/n(S) = P(A I B) = n(A I B)/n(S) = P(A|B) = P(A I B) / P(B) = Independent Events Two events are said to be independent of one another if the occurrence or nonoccurrence of one event has no effect on the occurrence or nonoccurrence of the other event. Two events A and B are said to be independent iff P(A I B ) = P(A) P(B) Ex. Let A be the event of an even number Let B be the event of a number at least 4 Are A and B independent? P(A) = P(B) = P(A I B ) = Multiplication Rule P(A I B ) = P(A|B) P(B)...
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## This note was uploaded on 02/15/2009 for the course STAT 2004 taught by Professor Melutz during the Fall '07 term at Virginia Tech.

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Lecture 11 - given that event B has already occurred is...

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