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
![[Image: MontyHallgood.jpg]](https://images.weserv.nl/?url=www.kitchentablemath.net%2Ftwiki%2Fpub%2FBloggers%2FMontyHallPart3LogPage%2FMontyHallgood.jpg)
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
Comparing the Universal Oneness of All Life to Yo Mama since 2010.
![[Image: harmlesskitchen.png]](https://i.postimg.cc/yxR97P23/harmlesskitchen.png)
I was born with the gift of laughter and a sense the world is mad.
I was born with the gift of laughter and a sense the world is mad.
