SEVERAL years ago, a reader wrote
to a columnist with a puzzle: Suppose you're on a game show,
and you're given the choice of three doors. Behind one door is
a car, the others, goats. You pick a door, say number 1, and
the host, who knows what's behind the doors, opens another door,
say number 3, which has a goat. He says to you, "Do you
want to pick door number 2?" Is it to your advantage to
switch your choice of doors?