OK think of it this way, when u choose 1 door out of 10, your
chance of hitting a car is what.......only 1 in 10, correct
anot.......Now when the host opens 8 other doors revealing goats,
that means now it's left with only 2 doors, your chosen door and
the remaining unopened door. One of them will have a car. Now how
confident are you that your originally chosen door, which has a 1
in 10 chance, actually has a car behind? Well the chance is only 1
in 10, not so good right? You're not so confident, right? But now
after the host elimitates 8 other doors, that means now the car has
to be behind one of the two doors. In other words, he has helped
eliminate other possibilities and improve the chance that the car
is actually at the other remaining door. By switching you are
taking advantage of this and improving your chance.
OK think of this another example.
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Suppose now there are 100 doors. Behind 1 door there is a car, the
other 99, goats. Now you choose a door, say door number 1. After
that the host opens 98 other doors revealing goats. He then ask you
whether you want to change your mind to switch to the other
remaining door. Is it to your advantage to switch?
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It's getting more and more clearer this way, use bigger and bigger
numbers.
