A Logic Problem
Consider this:
You are a contestant on a gameshow where the object is to win a car. The gameshow host shows you three doors and tells you that the car is behind one door and there are goats behind the other two. He asks you to pick a door. You pick a door but the gameshow host does not open that door. Instead he opens one of the other doors to reveal a goat (he knows which door the car is behind). He then gives you the chance to change your mind and pick the other unopened door instead. What should you do?
I reckon that you have greater odds of winning the car if you change, because I read about this problem in 'The Curious Incident of the Dog in the Night-time' and it makes perfect logical sense to me. Adam insists there is a equal chance of the car being behind either door.
What do you think?
You are a contestant on a gameshow where the object is to win a car. The gameshow host shows you three doors and tells you that the car is behind one door and there are goats behind the other two. He asks you to pick a door. You pick a door but the gameshow host does not open that door. Instead he opens one of the other doors to reveal a goat (he knows which door the car is behind). He then gives you the chance to change your mind and pick the other unopened door instead. What should you do?
I reckon that you have greater odds of winning the car if you change, because I read about this problem in 'The Curious Incident of the Dog in the Night-time' and it makes perfect logical sense to me. Adam insists there is a equal chance of the car being behind either door.
What do you think?
3 Comments:
There's a 100% chance the car is behind the same door it was at the start ...
(I hate maths.)
By
Jeangenie, at 5:10 pm
Aaagh - Adam thinks Stu's playing card example isn't the same problem as the gameshow one. I think we may have to agree to disagree as I can't convince him. :)
By
Lisa & Adam, at 10:08 pm
I think I have to agree with Adam. Once the door is opened to reveal a goat (a goat?), there are only 2 doors left, behind one is a car, behind the other, a goat. This is a new situation where there only two choices, not 3. Therefore each door has a probability of 1/2, so to change is as good as to stay.
Anyway, I'd prefer to win a goat.
By
Anonymous, at 11:17 am
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