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Unformatted text preview: Conditional Probability and Tree Diagrams Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15 . If the flight is on time, the probability her luggage will make the connection flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65. a) What is the probability that her luggage arrives on time? Answer: 0.695 b) Are the first flight leaving on time and the luggage making the connection independent events? NO Conditional Probability and Tree Diagrams A package will be picked up by one of 3 delivery vans, depending on which is nearest. The choices are equal for any of the vans to make the pick up. Past record for each van’s success in delivering packages are given as follows: • Prob(on time delivery for van 1) = .95 • Prob(on time delivery for van 2) =.96 • Prob(on time delivery for van 3) = .90. • What is the probability a package will be delivered on time? • Is package deliver independent of delivery van? • If package is delivered on time, what is the probability that it was delivered by Van 1? Bayes’ TheoremReversing the Conditioning ) ( )  ( ) ( )  ( ) ( )  ( )  ( c B P c B A P B P B A P B P B A P A B P + = At a gas station, 40% of customers pump regular gas , 35% pump midgrade gas , and 25% pump premium grade gas . Of those who pump regular, 30% pay at least $30 . Of those who pump midgrade, 50% pay at least $30 . And of those who pump premium, 60% pay at least $30 ....
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This note was uploaded on 03/27/2012 for the course STT 200 taught by Professor Dikong during the Spring '08 term at Michigan State University.
 Spring '08
 dikong

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