Each time a ball arrives at a junction in the maze, there is an equal chance (1 in 2) of it bouncing right or left. There is the same chance (or probability) as flipping a coin and getting a head or a tail. There is an equal chance of getting either.

This exhibit has seven possible outcomes. For a ball to land in leftmost tube it has to go left six times through the pipe maze. Similarly, there’s only one way a ball can get to the rightmost tube. The reason why more balls end up in the middle is because there are more paths the balls can take to the middle. There are twenty different paths a ball can take to get to the middle, for instance, it could go left three times, then right three times. What other ways can you think of for the ball to get to the middle tube? Since there are twenty different paths and each path is equally likely, you would expect to see twenty times as many balls in the middle tube as you do in one of the tubes on the end.

On average if you place 64 balls into the maze one will fall into each of the end tubes and twenty will fall into the tube in the centre.