Well, in that situation, what is your probability of winning? Well, there's three doors. The prize is equally likely to be behind any one of them, so there's three possibilities. One has the outcome that you desire. The probability of winning will be 1 3rd if you don't switch. Likewise, your probability of losing, well, there's two ways that you can lose out of three possibilities. It's going to be 2 3rd, and these are the only possibilities, and these add up to one right over here.