Ants and Triangle
There are 3 ants sitting on three corners of a triangle. All ants randomly pick a direction and start moving along edge of the triangle. What is the probability that any two ants collide?
Solution: Collision doesn’t happen only in following two cases A) All ants move in counter clockwise direction. B) All ants move in clockwise direction.
Explanation: Since every ant has two choices (i.e. either of the two edges going through the corner on which the ant is initially sitting), there are total 23 possibilities. Out of 23 possibilities, only 2 don’t cause collision. So, the probability of collision is 6/8 and the probability of non-collision is 2/8.
Answer: The probability of collision of the ants is 6/8