A game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat. What should you do (assuming you want the best odds of winning the car)?
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Difficult classic riddle-?
- Thread starter Q-man
- Start date
Green Greda SPACS
New member
You throw something metal over the door. if you hear a clink, thats the car, if you hear a goat sound, then umm, thats a goat
It's a classic probability question.
The odds say you should switch. At first you had a 1 in 3 chance of picking the door with the car, but think about it - If you picked the right door on your first pick, he's going to show you one of the other doors, to make you switch. And if you didn't pick the right door, the host isn't going to show you where the car is, now is he? If he does, game's over.
So if you switch doors, you actually then have a 2 in 3 chance of winning the car, as opposed to 1 in 3.
Think of it this way: When you first made your choice of doors, the chance that you picked the door with the car was 1 in 3, or 33%. The chance that you DIDN'T pick the right door was 2 out of 3, or 66%. Even after a goat is revealed, the odds that you didn't pick the right door at first are still the same - 66%. And since the host isn't going to open the door with the car, there's a 2/3 chance that the car is behind the door you can now switch to.
There was an argument about the probability of all this a few years back - it seems at first that since there are two doors left, your chance of winning a car, after a goat is revealed, should be 1 in 2, or 50%. But mathematically, you have to consider all the probable scenarios and outcomes - Marilyn Vos Savant (considered one of the smartest people in the world) wrote a column about this, and it raised some controversy.
A better explanation for this can be found at the link below.
This assumes a number of things - namely that the host KNOWS which door has the car, and that he will only open a door that doesn't have the car...
To expand on the point, look at "Deal or No Deal" - what do they have, like 50 suitcases? Your chance of picking the right case would be 1 in 50, or 2%. There's a 98% chance that you DIDN'T pick the right case. So if you open cases, and get down to 2 cases, 1 you picked and 1 you didn't, you should definitely take the money offered by the banker for your case. There's still just a 2% chance that you picked the million dollar case right off.
The odds say you should switch. At first you had a 1 in 3 chance of picking the door with the car, but think about it - If you picked the right door on your first pick, he's going to show you one of the other doors, to make you switch. And if you didn't pick the right door, the host isn't going to show you where the car is, now is he? If he does, game's over.
So if you switch doors, you actually then have a 2 in 3 chance of winning the car, as opposed to 1 in 3.
Think of it this way: When you first made your choice of doors, the chance that you picked the door with the car was 1 in 3, or 33%. The chance that you DIDN'T pick the right door was 2 out of 3, or 66%. Even after a goat is revealed, the odds that you didn't pick the right door at first are still the same - 66%. And since the host isn't going to open the door with the car, there's a 2/3 chance that the car is behind the door you can now switch to.
There was an argument about the probability of all this a few years back - it seems at first that since there are two doors left, your chance of winning a car, after a goat is revealed, should be 1 in 2, or 50%. But mathematically, you have to consider all the probable scenarios and outcomes - Marilyn Vos Savant (considered one of the smartest people in the world) wrote a column about this, and it raised some controversy.
A better explanation for this can be found at the link below.
This assumes a number of things - namely that the host KNOWS which door has the car, and that he will only open a door that doesn't have the car...
To expand on the point, look at "Deal or No Deal" - what do they have, like 50 suitcases? Your chance of picking the right case would be 1 in 50, or 2%. There's a 98% chance that you DIDN'T pick the right case. So if you open cases, and get down to 2 cases, 1 you picked and 1 you didn't, you should definitely take the money offered by the banker for your case. There's still just a 2% chance that you picked the million dollar case right off.
If you pick door one the host shows you door three, then you should choose door two for the best chance.
Here's why:
Part 1: The door you pick will have one of two things, a car or no car.
The chance of no car is 2/3
The chance of car is 1/3
Part 2: Since it is more likely that there is no car, then the host will show you another door also not containing the car.
Finally, the door not shown or picked must be the right answer.
Here's why:
Part 1: The door you pick will have one of two things, a car or no car.
The chance of no car is 2/3
The chance of car is 1/3
Part 2: Since it is more likely that there is no car, then the host will show you another door also not containing the car.
Finally, the door not shown or picked must be the right answer.