Suppose that you have a triangle with 3 ants on different vertices (corners) of the triangle. What is the probability that either 2 of the ants or all of the ants collide if all 3 ants start walking on the sides of the triangle?
The probability of the ants colliding is 0.75.
Each ant can move in 2 different directions. Because there are 3 ants, this means that there are 23 (8) possible ways that the ants can move.
Now, there will never be a collision between any of the ants if they are all walking in the same direction. And, the only time they will be walking in the same direction is if they are all walking either clockwise or counter-clockwise around the triangle. So, there are only two scenarios in which a collision will not happen between the ants.
This means that there are 6 scenarios where the ants will collide. And 6 out of 8 possible scenarios, means that the probability of collision is 6/8, which equals 3/4 or 0.75. Thus, the probability of the ants colliding is 0.75.