This is one of the good probability puzzle asked in interview questions. There are 3 ants on each corner of a triangle. At a given point of time they all start together for a different corner at random.What is the probability that they will not collide.

Well let’s see all the possibilities of this puzzle. there are total 8 possibilities for this puzzle in which the ants can move. Let us assume a triangle ABC. So the 8 combinations will be

  1.  A->B, B->C, C->A
  2.  A->B, B->A, C->A
  3.  A->B, B->A, C->B
  4.  A->B, B->C, C->B
  5.  A->C, B->C, C->A
  6.  A->C, B->A, C->A
  7.  A->C, B->A, C->B
  8.  A->C, B->C, C->B

So in these 8 possibilities there will be two non colliding movements
1 and 6.

So the probability will be 2/8 = 0.25.