There are three ants on a triangle, one at each corner. At a given moment in time, they all set off for a different corner at random. What is the probability that they don’t collide ?
See Solution : Ants on a triangleSolution 1:
Let the three ants are a, b, c.
So probability that they will not collide is 2/(2+6) i.e. 1/4
Solution 2 :
Total no. of movements: 8
A->B, B->C, C->A; A->B, B->A, C->A; A->B, B->A, C->B; A->B, B->C, C->B; A->C, B->C, C->A; A->C, B->A, C->A; A->C, B->A, C->B; A->C, B->C, C->B
Non-colliding movements: 2
A->B, B->C, C->A; A->C, B->A, C->B
(i.e. the all ants move either in the clockwise or anti-clockwise direction at the same time)
So probability of not colliding = 2/8 = 1/4