Alma and Bert and six other children will be arranged in a random order in eight seats. What is the probability that Alma is seated somewhere to Bert's right?
Use symmetry to solve.
Think of a possible arrangement of the eight children with A to the right of B. For example:
C, F, D, G, B, E, A, H
Then, there would be a "mirror image" arrangement:
H, A, E, B, G, D, F, C
in which A was to the left of B. For every arrangement in which A is to the right of B, there must be exactly one in which A is to the left of B. There's a 1-to-1 correspondence, so the two numbers are equal, and the probability is exactly 50%.