Tommy has a piece of toast that has butter on one side, and he dropped it twice. Both times, it landed with the butter side up. If he drops it 2 more times, what is the probability that it will have landed butter side up a total of 3 times?

First, note that since the previous drops have already happened, their result do not modify the occurrence of future results when the toast is dropped again.

In oder to have a total of three time landing butter side up, exactly, there are two possibilities:

Either the first next drop lands butter side up and the second next drop lands butter side down, or

The first next drop lands butter side down and the second next drop lands butter side up.

Since there are two ways of totaling side up 3 times, you have to sum both chances.

1) Next drop butter side up and second drop butter side down:

1/2 × 1/2 = 1/4

2) Next drop butter side down and second one butter side up:

1/2 × 1/2 = 1/4

3) Add both probabilities: 1/4 + 1/4 = 1/2

And that is the answer: 1/2