(January 12, 2013 at 9:07 pm)Rev. Rye Wrote: Well, since this thread's been resurrected and I haven't heard any mention of "The Curious Incident of the Dog in the Night-Time", I'll explain it as Christopher Boone explained it.
Let the doors be called X, Y and Z.
Let Cx be the event that the car is behind door X and so on.
Let Hx be the event that the host opens door X and so on.
Supposing that you choose door X, the possibility that you win a car if you then switch your choice is given by the following formula
P(Hz ^ Cy) + P(Hy ^ Cz)
= P(Cy)·P (Hz ¦ Cy) + P(Cz)·P(Hy ¦ Cz)
= (1/3 · 1) + (1/3 · 1) = 2/3
I would note Monty Hall himself has addressed this problem. He pointed out that the odds are not 2/3 for a very simple reason: he was allowed (and often did) to influence the decision-making (do I change or switch) through manipulation of the contestants.
For his description, see his own Website, Let's Make A Deal: The Monty Hall Problem
"Be ye not lost amongst Precept of Order." - Book of Uterus, 1:5, "Principia Discordia, or How I Found Goddess and What I Did to Her When I Found Her."
