Ok , Let's have some problem . There are 3 ants on an equilateral triangle and they can move in either direction , what is the probability that they will never intersect and what is the probability that any two of them will intersect.

Question

Sarfraaz Msa · Accepted Answer

0.5 they can intersect
0.5 they cannot intersect

Soumya Ranjan Nayak · Answer

2 out of 8  times they will not be colliding, as they all will be moving in same direction. So 6/8 times they will collide. 0.25 is the probability that they will not collide provided the triangle is equilateral and  all ants are moving in the same speed.

Kartik Negi · Answer

1. Probability of no collision
     No collision will happen only if all the ants move clockwise or anti-clockwise.
     An ant can move only in 2 directions, therefore, the probability of an ant moving in one direction = 0.5
     For three ants, 0.5*0.5*0.5 = 1/8 (for clockwise)
     Similarly for anti- clockwise = 1/8
     For no collision, either ants will move together in clockwise or anti-clockwise direction
     Therefore, 1/8 + 1/8 = 2/8 or 0.25
     There is a 25% chance that there will be no collision and 75 % chance that any two of them will intersect.

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