There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.

What is the probability that they don't collide?

Answer

Let's mark the corners of the triangle as A,B,C. There are total 8 ways in which ants can move.

1. A->B, B->C, C->A

2. A->B, B->C, C->B

3. A->B, B->A, C->A

4. A->B, B->A, C->B

5. A->C, C->B, B->A

6. A->C, C->B, B->C

7. A->C, C->A, B->Ajavascript:void(0)

8. A->C, C->A, B->C

Out of which, there are only two cases under which the ants won't collide :

A->B, B->C, C->A

A->C, C->B, B->A

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