05 Cond Prob - Mult - Ind

05 Cond Prob - Mult - Ind - Today Conditional Probabilities...

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3/26/10 Today Conditional Probabilities Independence Multiplication and Total Probability rules Next week Monday: Examples, Bayes Theorem Homework due on Wed., and review Test Friday
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3/26/10 Conditional Probability It is often useful to be able to calculate the probability of some event given that some other event has occurred. Example Experiment: Flip 3 coins. S = {HHH, HHT, HTH, …}
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3/26/10 Conditional Probability The following is very important: Definition of Conditional Probability The above equation is the definition of ) ( ) ( ) | ( B P B A P B A P =
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3/26/10 Conditional Probability Definition of Conditional Probability ) ( ) ( ) | ( B P B A P B A P = A B A
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3/26/10 Example 1 Returning to the example above: Flip 3 coins. A = 2 or more heads B = first coin is head What is Pr{A|B}
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3/26/10 Example 2 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?
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3/26/10 Example 3 random. Find the following using the definition of conditional probability. a) P(IE) = b) P(female) = c) P(IE and Female) = d) P(MATS and Female) = P(IE|Female) = Male Femal e Total IE 11 7 18 MatSci 5 3 8 ChE 4 1 5 Total 20 11 31
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3/26/10 Example 4 Suppose we roll two dice. Let d1 and d2 represent the two outcomes.
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05 Cond Prob - Mult - Ind - Today Conditional Probabilities...

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