How do I work out probability when a random choice is repeated?

Before you try to work out the probability, establish the following answers from the question and jot them down. How many items are there in total? After something is chosen, is it put back before the next choice? The answers to these determine the denominator (bottom number) of the fractions in your probability tree. On the first set of branches, the denominator is the total, n. On subsequent, if the item is replaced, it is also n, or if it isn't then the denominator will reduce by 1 with each set of branches. The numerator for the first set of branches is the number of each type set out in the question. For subsequent, if the item is replaced, this doesn't change. If the item isn't replaced, then numerator for the type chosen first decreases by one and the others don't change.

Once you have your probability tree drawn out in this way, calculate probabilities by multiplying along branches, or adding between them if there's several ways that the event specified could occur.