I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Saturday, August 20, 2005
Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?
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yeah it is to your advantage because you aren't really losing anything by picking another door. i mean you are either going to get another goat (wjich you had in the first place) or you could end up with a car.ReplyDelete
Good answer. But I was thinking of not just losing out, but gaining!ReplyDelete
This question was asked by Craig Whitaker in the "Ask Marilyn" in Parade Magazine in 1996. Marilyn's answer got quite a backlash, but it turns out she got it right.ReplyDelete
If you switch to the other door, instead of having a 1 in 3 chance of winning, you'll have a 2 in 3 chance! The idea is simple but quite counterintuitive. By making a "blind" choice between the three doors, you have a 1 in 3 chance of being right, but a 2 in 3 chance of being wrong. Then door 3 is removed. By switching away from your first choice to door 2, you'll now have a 2 in 3 chance of being right!
If you'd like to try out this answer in an interactive way, use cards instead of doors. Always switch away from your first choice. If you keep track of how many times you get the "prize", you'll see soon enough that Marilyn got it right!ReplyDelete
You might also try searching on the web for the "Monty Hall" problem.