Here is an infamous question that has a right answer. See if you can figure it out. If you can, tell me why you are right.
Note: To anyone who recognizes the question and already knows the answer, please don't spoil it for others!
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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Best answer gets 10 points
2007-08-06 17:21:46 · 7 answers · asked by Anonymous in Entertainment & Music ➔ Jokes & Riddles
No one's gotten it so far... Keep guessing, y'all are close!
2007-08-06 17:41:00 · update #1
Yes you have the advantage. If you keep the same choice your odds of winning are 1 in 3. If you switch your choice your odds of winning are 2 in 3. This is because you had a 2 in 3 chance of being wrong the first time when "door 3" was opened. If you guessed a goat on the first attempt (2 in 3 chance), the game show announcer is not going to open the door with the car, so by definition if you switch you are guaranteed to win. So you had a 2 in 3 chance of winning if you switched!
2007-08-06 19:30:58 · answer #1 · answered by Mayday 2 · 1⤊ 2⤋
It makes no difference - it is *neither* for or against your interest. After the goat is revealed, you then have a 50% chance regardless whether you stick with your first pick, or switch to the other remaining door.
The confusion here is about the meaning of "a priori" and "a posteriori" probabilities.
Whichever door you picked in the beginning, you had a 1/3 chance (a priori probability). However that chance immediately went up to 1/2 when one goat was revealed (a posteriori probability).
(Conversely if they revealed the position of the car to be behind another door, the a posteriori probability of your first guess would then be 0. But you would of course switch it, in that scenario.)
The key point here is that the probability of your choice winning goes up from 1/3 to 1/2 when one of the losing choices is eliminated, regardless what you do or don't do
(ok obviously we exclude you picking the known goat).
(Discounting purely silly answers like "the goats and car can move", or "the goat might be very obese and standing in front of the car, but occupying a different door" (Jabba the Goat scenario) :) )
2007-08-06 18:25:30 · answer #2 · answered by smci 7 · 1⤊ 1⤋
yes it is advantageous. If you decide to stick with your choice of door 1 throughout the game, then you have a 1/3 chance in winning, since there are three doors and opening the goat door doesn't affect your choice. But, if you decide to switch, you now have a 50/50 chance at winning because there are only 2 doors and one of them has a car.
or how about:
Yes it is an afvantage becuz in the beginning, it's a 2/3 chance to get a wrong door. Then, when he shows you the wrong one, you should switch to get the car.
But, in the beginning, it's a 1/3 chance of getting car, then the guy shows you the wrong door, you switch, and get a bad prize.
So- the 2/3 chance of getting a wrong door is more likely to happen, and you shoould switch.
2007-08-06 17:27:18 · answer #3 · answered by Anonymous · 1⤊ 1⤋
yes, if you switch your choice you have a 50/50 chance of winning sice now it can be either a goat or a car
2007-08-06 17:35:19 · answer #4 · answered by Kokomoe 2 · 0⤊ 2⤋
No....because he's trying to trick you into thinking door 2 has the car....???
2007-08-06 17:28:44 · answer #5 · answered by Anonymous · 0⤊ 1⤋
no, it is not in your best interest to switch your answer.
2007-08-06 17:59:02 · answer #6 · answered by tlundberg04 1 · 0⤊ 1⤋
ya, id rather have nothing than a goat, it would just crap all over the place
2007-08-06 17:47:04 · answer #7 · answered by ♥...........♥ 5 · 0⤊ 4⤋