Ant And Triangle Puzzle

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Ant And Triangle Puzzle

Ant And Triangle Puzzle

Question:

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?

Answer:

0.25

As the condition is none of the ants should collide ,it is only possible if all ants move in clockwise or anticlockwise direction.

As ants can move only in two directions.

 P(clockwise)=Probability that all ants move in clockwise direction is = 0.5*0.5*0.5 =0.125

P(clockwise)=Probability that all ants move in anticlockwise direction is = 0.5*0.5*0.5=0.125

P(No collision) = P(All ants go in a clockwise direction) + P( All ants go in an anti-clockwise direction) = 0.125 + 0.125 = 0.25