# Ant and Triangle Problem

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Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?

vipin Scholar Asked on 26th July 2015 in

The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). If the ants do not pick the same direction, there will definitely be a collision. Each ant has the option to either move clockwise or anti-clockwise. There is a one in two chance that an ant decides to pick a particular direction. Using simple probability calculations, we can determine the probability of no collision.

N(No collision) = N(All ants go in a clockwise direction) + N( All ants go in an anti-clockwise direction) = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5 = 0.25

vishal Scholar Answered on 28th July 2015.

Somewhat more simply stated: pick an ant.  Each of the other two ants must decide to go the same direction which is 0.5 * 0.5 = 0.25.

dougbell Genius Answered on 21st October 2015.

There are two possibilities if all the ants move in clockwise or counterclockwise direction, they wont collide.
The total no. of case that can happen is 2*2*2 where each ant can choose either of the directions.
So the probability is 2/8=0.25

psn Guru Answered on 8th December 2015.

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