Three ants sit at the three vertices of an equilateral triangle. At the same moment, they all start moving along the edge of the triangle at the same speed but each of them randomly chooses a direction independently. What is the probability that none of the ants collides?
Each ant has a half-half chance to choose either the clock-wise or the counter-clock-wise direction. They will not collide if and only if all of them happen to choose clock-wise direction or all of them happen to choose counter-clock-wise direction. Given that each ant has a probability of $0.5$ to choose clock-wise direction, the probability that all of them choose this direction equals $$0.5\times 0.5\times 0.5=0.125$$
Similarly, the probability that all of them choose counter-clock-wise direction is also $0.125$. Therefore, the final result is $$0.125+0.125=25\%$$