There are $24$ ants scattered around a hula hoop of circumference $3$ meters . They each randomly, and independently, choose to face clockwise or counterclockwise, and then simultaneously start marching at $1$ cm/sec. When two ants meet, they instantaneously reverse direction.
Let's say that one of the ants is named Alice. After $5$ minutes of marching, what is the probability that Alice is back where she started?
Note: I have changed the number of ants from $25$ to $24$. This doesn't affect how you approach/solve the problem, but makes the answer more interesting.