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Ants - do not collide

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?

SOLUTION : The only way to avoid collision is that all ants move clockwise or all ants move anticlockwise, otherwise a collision is certain. Now, each ant can pick any direction randomly, so a total of 2x2x2=8 cases are possible. This is just like that when you toss 3 coins; there are 8 possible outcomes possible.

The probability to not collide will be favorable cases/total cases = 2/8 = 0.25

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