No explanation worked for me. I did a truth table, and said, "...huh."
You don't need to model all three door choices. Just say you pick Door A, not Door 1. The first door you didn't pick is B, and C is the other door. Then map the prize behind each of 3 doors, and whether you stay or change your answer.
Then count the number of successes for change versus stay. Spoilers: It's 3/6 vs 2/6.
You don't need to model all three door choices. Just say you pick Door A, not Door 1. The first door you didn't pick is B, and C is the other door. Then map the prize behind each of 3 doors, and whether you stay or change your answer.
Then count the number of successes for change versus stay. Spoilers: It's 3/6 vs 2/6.