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- Aug 3, 2003

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a) You pick door one and the host (who has a choice of two doors) opens door two, switching will give a lose.

b) You pick door one and the host (who has a choice of two doors) opens door three, switching will give a lose.

c) You pick door two, and the host has no choice but to open door three, switching will give a win.

d) You pick door three, and the host has no choice but to open door two, switching will give a win.

These are the only four possible scenarios, and there will still be two win situations and two lose situations whichever door the car is behind.

I think where people are going wrong is in forgetting that if you choose the car door outright, then the host has two choices of action both of which will result in switching being a lose - missing one of those out suggests that switching will give a win in 2/3 switches, when it is actually 2/4.