Questions
- Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Solutions
The ants can only avoid a collision if they all decide to move in the same direction (either clockwise or anti-clockwise). So what is the probability of taking Clockwise direction? 1/2 (0.5).What is the probability of all ants taking the same direction?
Probability of taking the Clockwise direction = 0.5x0.5x0.5 Probability of taking the Anti-Clockwise direction = 0.5x0.5x0.5 Probability of taking the Same Direction = 0.5x0.5x0.5+0.5x0.5x0.5=0.125+0.125=0.25