Puzzle: 3 ants problem

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There are three ants on different vertices of a triangle What is the probability of collision (between any two or all of them) if they start walking on the sides of the triangle?

Similarly find the probability of collision with "n" ants on an "n" vertex polygon
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By  Vineet JhunJhunwala





Sangeeta Haldhar Sangeeta Haldhar   11 years ago

Ant can go clock wise and anticlockwise
so one ant have a both direction to go and second and third also.

so collision = 3 ant go clock wise + three ant go anti clock wise
1/2 * 1/2 * 1/2 + 1/2 * 1/2 * 1/2
= 0.25

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Roshan Singh Roshan Singh   11 years ago

Every Ant can move in 2 possible directions , backward and forward ( B or F ) , so the whole sample space consists of 8 choices, out of which 2 , namely BBB and FFF are no collision choices.
So probability of not colliding is 2 /8 = 1/4 = 0.25
Sample space:
F F B
F F F
F B B
F B F
B F B
B F F
B B B
B B F
So probability of colliding is = 1 - 0.25 = 0.75
In general case(for 'a' ants on 'a' vertices):
total outcomes = 2 x 2 x 2 x ...a = 2ª
no collision = 2
probability of no collision = 2/2ª
So, probability of collision = 1 - 2/2ª

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