Originally posted by trad
You're on a game show in front of three doors, behind two of them there are goats and behind the other one is a car. You must pick a door and win whatever is behind. After you pick a door (say #1) the host opens another door (say #3) and shows a goat, he then offers you the chance to switch doors (to #2 instead of #1)... should you switch? (demonstrate why or w ...[text shortened]... door.
- If the player initially chose the car door, the door uncovered by the host is random.
Ah ha a nice counter intuitive problem that illustrates the hard wierd non logical way in which our minds work (or not work as is more reasonable to say).
The first choice gives us a 1in 3 probability of choosing the car. Then through being presented with the option of switching we reason intuitivly that we now have a 50:50 probability in choosing the car.
However the true probability(at least in a mathematical definition of the system) is 2 in 3.
We have simply choosen 2 out of the 3 boxes.
So we should always switch.
You have all fallen into the intuitive mistake when visualising the problem. . . . .In saying that the final probability is 50:50 by breaking the problem into two distinct choices.