Point Path Probability

Consider a 25*25 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 ?

1 Answers

Manish Shankar ·

In going from bottom to top you to travel 24 horizontal lines and 24 vertical lines.

Total point that you will cover is 48+1=49

So Prob=49/625

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