07.1 Cond Prob - Mult - Ind

# 07.1 Cond Prob- - Today Independence Multiplication and Total Probability rules Finish Independence Go over HW Test on Friday not Wed Friday Next

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1/5/10 Today Independence Multiplication and Total Probability rules Friday Finish Independence Go over HW Next week

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1/5/10 Conditional Probability The following is very important: Definition of Conditional Probability If the event B occurs… ) ( ) ( ) | ( B P B A P B A P =
1/5/10 Example An organization is running a dinner for employees with at least one son. Given that Ms. Jones is invited to the dinner, what is the probability that both her children are boys? S = { (bb) (bg) (gb) (gg)} P(bb|at least 1 boy) = P(bb and at least 1 boy)/P(at least one boy) P(bb and 1b) = ¼ P(1b) = ¾ P(bb|1b) = 1/3 So we see that the sample space we wanted has 3 outcomes, not the 2 we mistakenly assumed at first. Given that the one child was a boy, we only eliminate gg from the space.

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Multiplication Rule Useful in determining the intersection of sets. ) ( ) | ( ) ( ) | ( ) ( A P A B P B P B A P B A P = = An urn contains 8 red balls and 4 white balls. We draw 2 balls without replacement. Assume at each draw, each ball has equal probability of being chosen. What is the probability that
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## This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.

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07.1 Cond Prob- - Today Independence Multiplication and Total Probability rules Finish Independence Go over HW Test on Friday not Wed Friday Next

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