# A triangle has a bug on each corner. If each walks in random direction, find probability of no bug crashs with other?

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There is an equilateral triangle and three bugs are sitting on the three corners of the triangle. Each of the bugs picks up a random direction and starts walking along the edge of the equilateral triangle. What is the probability that none of the bugs crash into each other?

posted Mar 31, 2017

+1 vote

Out of the eight possible outcomes ( 2×2×2 ) only 2 possibilities ( All the ants moving clockwise or anticlockwise ) allow the ants to not cross path with each other. Therefore the probability that the ants won't crash each other on this scenario is = 2/8 = 1/4 = 25%.

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