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?

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    If you have come up with the fact that the bugs can avoid the collision only when they decide to move in the same direction be it clockwise or anti clockwise, you have already solved half of it. In any other way, the bugs will definitely run into each other.

    Now the bugs can move either clockwise or anti-clockwise. The probability of choosing a specific direction is then 1/2.

    We will utilize the simple equation of probability to find out our answer

    P(No Collision) = P (The bugs move in clockwise direction) + P(The bugs move in anti-clockwise direction)
    = 0.5 * 0.5 * 0.5 + 0.5 * 0.5 * 0.5
    = 0.25

    Thus the probability that the bugs won’t collide into each other is 0.25 or 1/4.

    ravi Expert Answered on 19th July 2015.
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