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A probability question:

Two friends agreed to meet in a coffee shop in the time interval of $9:00AM-10:00AM$. Each one is coming on a random time in this interval, and stays for 10 minutes.

What is the probability that they will meet?

My try:

Denote $X$ as first friend coming time and $Y$ as second friend coming time. $X, Y$ ~ $U(0,60)

I need to find $P(|X-Y| < 10) = P(X - Y < 10) + P(Y - X < 10)$

Start: $P(X - Y < 10) = (X < 10 + Y) $

Drawing a triangle gives a probability of $\frac{12.5}{200}$.

But it's not one of the possible answers. Can you help me please? Thanks in advance.

Billie
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  • Related: http://math.stackexchange.com/questions/680/probability-that-two-people-see-each-other-at-the-coffee-shop - draw the square, shade the digonal stripe and work out the ratio of areas – Henry May 11 '15 at 00:27
  • Also related: http://math.stackexchange.com/questions/462851/lunch-meeting-probability-for-two-person-to-meet-in-given-1-hour-slot-and-none-w and http://math.stackexchange.com/questions/680573/probability-of-two-persons-to-meet and math.stackexchange.com/questions/800053/continuous-probability-about-meeting-between-two-friends and http://math.stackexchange.com/questions/936951/probability-that-a-meets-b-in-a-specific-time-frame – Henry May 11 '15 at 00:32
  • @Henry Great! $\frac{11}{36}$. A moderator can redirect this question to Henry's link. Thank you!! – Billie May 11 '15 at 00:38

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