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Mon 5 Jun, 2006 01:22 pm
Please explain this question and its answer, thank you
You start at a corner of 5 blocks south and five blocks west of your friend. You walk north and east while your friend walks south and west at the same speed. What is the probability that the two of you will meet on your travels?
thank you.
There are a number of paths that each of you can take. Some of them will cause you to meet. Figure out the ratio to compute the probability.
You can only meet on the NW/SE diagonal (these points are five blocks from each person). The number of ways for each person to get to these six intersections is 1, 5, 10, 10, 5, 1 (look familiar?).
The probability that each shows up at the same intersection is:
(1^2 + 5^2 + 10^2 + 10^2 + 5^2 + 1^2) / 32^2 = 252/1024 = 63/256
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