Uniform distribution: 2 friends meeting between 1pm 2pm

Ryan2009

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Mar 23, 2009
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Two friends decide to meet at the Diamond Plaza between 1 pm and 2 pm. They cannot meet before 1 pm or after 2 pm. The one who comes to the meeting point first must wait 10 minutes for the other one. If the other person does not show up within 10 minutes, then he can leave. For example, A comes first at 1:13. He waits till 1:23. If B does not show before 1:23, then A leaves the meeting point. Assuming that the distribution of time of arrival between 1 pm and 2 pm is uniform for both persons, what is the probability that they will meet?
 
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