(March 13, 2016 at 8:19 am)robvalue Wrote: Er... what?
I don't understand you. Yes, this whole thread has been explaining why you change.
The only assumption I make is that the prize has initially been selected randomly to be behind one of the doors.
If I chose wrong initially, with 2/3 chance, I will guarantee to win if I change.
If I chose right initially, with 1/3 chance, I will lose.
Chances I win = (2/3) * 1 + (1/3) * 0 = 2/3
It's how you calculate the mean of a probability distribution.
The math is all very fascinating rob, too bad you'll be returning home with a goat. The car was behind door 1.