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July 2, 2015

Homework Help: maths

Posted by rishabh on Monday, June 10, 2013 at 10:54pm.

Consider a 2525 grid of city streets. Let S be the points of intersection of the streets, and let P be the set of paths from the bottom left corner to the top right corner of which consist of only walking to the right and up. A point s is chosen uniformly at random from S and then a path p is chosen uniformly at random from P. Over all (s,p) pairs, the probability that the point s is contained in the path p can be expressed as ab where a and b are coprime positive integers. What is the value of a+b?

Details and assumptions
There are 25 streets running in each direction, so S consists of 625 intersections.

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