Casino Coffee
Maths probability problem?
Mike and Dougal are going to the casino. They agree to meet at a coffee shop near by. Each arrives randomly at a time between 8.00pm and 8.30pm. They have agreed to wait for 5 minutes for the other to arrive. If after 5 minutes the other person has not arrived they leave and go to the casino alone. What is the probability that Mike and Dougal meet?
Can you please show working/ explain because i'm really cabbage at maths. Thanks soooo much!!!
This is maybe the most well known geometric probability problem, cited in many sources ('Meeting Problem'). Let x and y are the moments past 8:00 of arrivals of both persons:
0 ≤ x ≤ 30, 0 ≤ y ≤ 30
All possible cases can be illustrated by all points with coordinates (x, y) in a square with side 30:
http://farm4.static.flickr.com/3639/3672223992_ec992a35bd_o.gif
The meeting will take place if both moments differ with 5 at most:
|x - y| ≤ 5, so the favorable cases are the above points in the stripe
-5 ≤ x - y ≤ 5 (green points on the picture)
Now the required probability is
Area(green hexagon) / Area(square) =
= 1 - Area(both gray triangles) / Area(square) =
= 1 - 25² / 30² = 1 - 625/900 = 275/900 = 11/36
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