Unformatted text preview: one of the events A , B happens is P ( A ) + P ( B )2 P ( AB ) (c) Show that if the events A and C are conditionally independent given B i.e., P ( AC  B ) = P ( A  B ) P ( C  B ) then P ( A  BC ) = P ( A  B ) 3. A commuter train departs at a random time between 12:00pm and 1:00pm. Also, during 20 marks the same onehour period, a bus arrives at the commuter train station at a random time. A random experiment consists of recording the pair ( T 1 ,T 2 ) of the train departure time and the bus arrival time. (a) Find the sample space of this experiment and sketch it on the ( x,y )plane. (b) Find the probability that the bus will arrive at the station at the same time as the train leaves. (c) Find the probability that the bus will arrive at the station before the train leaves. (d) Find the probability that the bus will arrive at the station at least 5’ before the train leaves. 1...
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 Spring '09
 Champagne
 Probability, Probability theory, commuter train departs, commuter train station

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