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Wait between five and ten minutes for the other to arrive

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1. * (Probability of a Diamond). Suppose X; Y; Z are independent U Œ-1; 1] variables. Find the probability that jX jC jY jC jZj ::= 1:

2. (Missing the Bus). A bus arrives at a stop at a random time between 9:00 AM and 9:15 AM. Tim will arrive at that stop at a random time between 9:00 AM and 9:15 AM, independently of the bus, and will wait for (at most) five minutes at the stop. Find the probability that Tim will meet the bus.

3. Cathy and Jen plan to meet at a cafe, and each will arrive at the cafe at a random time between 11:00 AM and 11:30 AM, independently of each other. Find the probability that the first to arrive has to wait between five and ten minutes for the other to arrive.

Reference no: EM13983763

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