Game One: You are given a choice of three doors. You pick number one. The host opens one of the other two doors, having been given instructions that, if you pick the car, the host is to open one of the other doors, and if you pick a goat, the host opens the other door with a goat. Stalemate. It is a predetermined outcome.
Game Two: The prior game’s outcome stands. The new choice you have is do you keep door number one, or do you switch?
How do you have a 2/3 chance of winning if you switch?
In: 107
There are two common erroneous assumptions made about the problem as presented. The first is that the host acts randomly when host has full knowledge. Second, the host does not open one door, the host opens all unselected non-winning (goat) doors.
This is shown more clearly and is more intuitive when the example is expanded:
The contestant is presented with 100 doors, there are 99 goats and 1 car behind them. They pick #3 (1/100 chance). The host shows all doors except #88 is goat. Now, does contestant stay with #3(still 1/100 chance) or switch to #88, effectively picking all other doors (99/100)? There is no chance the host chose a goat behind #88 unless there was no car available (because it was behind #3).
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