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Probability that two people will meet within 10 minutes

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Two people decide to meet in lobby of hotel between 11:30 and 12 noon. If they arrive at random times during this period, what is the probability they will meet within 10 minutes?

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The expert examines the probability that two people will meet within 10 minutes.

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The problem can be solved by using uniform distribution. Let X and Y be the arrival times of two persons, then it is uniformly distributed on the interval (0, 30). Hence the probability density of X and Y is given by

Since the person is coming independently the joint distribution of (X, Y) is given ...

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