The game show problem
August 31st, 2008 by KenricWhile watching the movie “21″ this past weekend the professor character in the movie posed the infamous game show question.
There are 3 doors for a contestant to choose from. Behind one door is a new car and the other two are goats. The contestant chooses door #1. The host, who knows which door the car is behind then opens one of the unchosen to reveal a goat. The host now asks the contestant if he would like to change doors. Should the contestant keep door #1 or change doors?
The answer is that the contestant should always change doors.
Posted in General | 6 Comments »
Stumble it!
no you are infact wrong, the movie is correct. Its mathematical probability.
Initially you have a 33% chance of your door being the car.
He opens another…goat…
the other unopened door still has a 33% chance of being the car, but now yours has 66.66%. (1-0.333)
B.Eng
By ben on Sep 1, 2008
Ben, I think you are agreeing with me? In the movie he said you should switch to the other door and that’s what I’m saying.
When you picked the 1st door you have a 33% chance of selecting the correct door.
Now that the host has shown you an incorrect door it does not change the fact that when you chose door #1 that it had a 33% chance of being correct. However, what does change is that the other door has a 66% chance of being correct so therefore switching doors gives you a 66% chance of being correct.
By Kenric on Sep 1, 2008
I would say that with a 66% chance of winning a car I would think really hard and then probably switch my choice. This is one of my favorite game show questions that I’ve actually had a few professors in the past ask. Thanks
By Self Directed IRA on Sep 3, 2008
Isn’t this something of a faulty premise? After the first door is opened, the odds are at 50/50 because your chances are now 1 out of 2.
Did anyone watch “Deal or No Deal” the other night? A pregnant woman finally won the $1 million prize. She picked a briefcase (out of 26 briefcases) at the beginning of the show and, by opening them one at a time, narrowed it down to the briefcase she picked and another one she didn’t pick. She kept the one she originally picked (when offered the chance to switch them) and she won the $1 million.
By ubu50 on Sep 4, 2008
Below “O” is the car.
1 2 3
O X X
If you never ever switch, the only way you can win is if you pick door #1. 1 out of 3, Agreed?
If you always switch, the only way you can lose is if you pick door #1. 2 out of 3, Agreed?
Let’s say you pick 1, the host takes away 2.
you stay with 1 = you win
you switch to 3 = you lose
Let’s say you pick 2, the host takes away 3.
you stay with 2 = you lose
you switch to 1 = you win
Let’s say you pick 3, the host takes away 2.
you stay with 3 = you lose
you switch to 1 = you win
By Kenric on Sep 4, 2008
BTW, this doesn’t work with Deal or No Deal because Howie doesn’t remove only the low dollar suitcases. If he did, you’d keep going until the end and then switch.
By Kenric on Sep 4, 2008