3 Ants at triangle's corners

♠ Posted by GeekyFry in , at 10:14 AM

There are three ants residing at the three corner of a triangle. After some point of time they will change their position and move for another corner. What is the probability that they will not collide?



Possible Solution:

The ants would avoid a collision if they all start to move in the same direction (either clockwise or anti-clockwise).
If the ants do move in the same direction, there will definitely be a collision.
Each ant can 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.
P(No collision) = P(All ants go in a clockwise direction) + P( All ants go in an anti-clockwise direction) = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5 = 0.25

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