You arrive at a bus stop at 10 oclock, knowing that the

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QUESTION:

You arrive at a bus stop at 10 oclock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. What is the probability that you will have to wait longer than 10 minutes? If at 10:15 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

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QUESTION:

You arrive at a bus stop at 10 oclock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. What is the probability that you will have to wait longer than 10 minutes? If at 10:15 the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

ANSWER:

Step 1 of 3

Given that Bus arrives uniformly at the bus stop between  and . Let  denote the arrival of bus at the bus stop. Then,  is a uniform random variable having density as

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