N ants are randomly placed on a circle with diameter of 1m. Each ant starts walking along the circle at a random direction, clockwise or counter-clockwise. All ants walk at the same speed, 1m/sec and when two of them meet, they bounce off each other and change direction. One of the

ants is named Alice. Can you calculate the probability that Alice is back to the point where she started, 1 minute after the ants start

walking?