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?
From “Ask Marilyn” column in Parade magazine in 1990 as quoted on the Monty Hall problem on Wikipedia [ via Keith Devens ]
I won’t give away the answer, but I will say that there is a specific choice that leads to a greater probability of getting the car. The Wikipedia page covers this in surprising detail.
One reply on “The Monty Hall Problem”
This is my take on it…
The odds of getting it right are 1/3.
Everyone seems to think that they end up being 1/2, but that’s only if you make a selection after one choice has been removed – which is effectively what you are doing when you switch.
So when you change your mind, you get a 1/2 change of getting it right. If you don’t you get a 1/3 chance of getting it right since he was always going to show you a goat.
:J