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Digital Dice by Paul J. Nahin

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2. Will Lil and Bill Meet at the Malt Shop?

Let’s denote the arrival times of Lil and Bill by L and B, respectively, where L and B are taken as independent and uniformly distributed random variables over the interval 0 to 30 (0 means arriving at 3:30 and 30 means arriving at 4 o’clock). Obviously, if L < B, then Lil arrives first, and otherwise (L > B) Bill arrives first. So, we can now immediately write

 

 

if L < B, then Lil and Bill will meet if B — L < 5

and

 

 

if L > B then Lil and Bill will meet if L — B < 7.

Figure S2.1 shows the geometric ...

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