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Two people agree to meet each other on a particular day, between 5 and 6 PM, They arrive independently on a uniform time between 5 and 6 and wait for 15 mintues. What is the probability that they meet each other ?

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    _Draw_ a sketch of the $x$-$y$ plane with a square with opposite vertices $(0,0)$ and $(1,1)$. The point $(X,Y)$ within this square gives the times of arrival of the two people. Mark the region of the square containing all the points for which $|X-Y| \leq \frac{1}{4}$. The area of this region is the desired probability. You don't _have_ to evaluate an integral to find the area. Simple mensuration (area of triangle $= \frac{1}{2}\times$ base $\times$ altitude will suffice).2012-12-03

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