Subsets of sample spaces

Anna and Charles have a bag that contains $1$‍ black marble and $1$‍ white marble. They are playing a game where they randomly select a marble out of the bag three times, with replacement.

Anna thinks that the probability of getting a black marble on the first selection and a black marble on the third selection is greater than the probability of getting a black marble on the first selection and a white marble on the third selection. Charles disagrees. He thinks that the two probabilities are equal.

The sample space of possible outcomes is listed below. B represents a black marble, and W represents a white marble.