LogFAQs > #939672627

Maybe I can break some brains if I point out that the guy who says it's 50/50 at the second selection is technically right, and here's why. There's a 2/3 chance that switching in general will win you the car. There's a 1/3 chance that keeping your door in general will win the car. Choosing randomly, that means we'll switch half the time and keep half the time. That means that, by chance, we'll still switch doors and win 1/3 of the time and that, by chance, we'll keep doors and win 1/6 of the time, meaning we'd still expect to win 50% of the time choosing randomly.

Note, however, that a 50% probability of you winning isn't the same as saying it doesn't matter which one you pick. If I have a recording of this year's Super Bowl and play it out, the Chiefs will win 100% of the time. If I say the Chiefs will win, I'll be right 100% of the time. If I say the 49ers will win, I'll be wrong 100% of the time. If I flip a coin, I'll still be right half the time but it's not the same as saying it doesn't matter which one I pick.