*Originally posted by swisscheese*

**please explain in eng.**

Which bit stumped you? Here's the table with attempted more correct spacing (hard to do with the pesky blank space contraction here)

1st pick....Host opens....Car revealed by host?....correct to switch?

...door a......door b........................no.........................no.........

...door a......door c........................no..........................no.........

...door b......door a.......................yes.....................irrelevant....

...door b......door c........................no..........................yes........

...door c......door a.......................yes.....................irrelevant....

...door c......door b........................no..........................yes........

The point is that now the host doesn't know where the car is he

*might reveal the car by accident* - which gives us the rows marked irrelevant in the table, since you would have no chance to switch if he did that. Because you know he hasn't revealed the car this increases the chance that your first choice was right.

Think of it as a bag with 99 black balls in and one red ball. With your eyes closed you reach in and take a ball and the host hides it without showing you its colour. You know you are very unlikely to have randomly picked the red ball.

If the host now looks in the bag and carefully removes 98 black balls, you know the ball remaining in the bag is very likely to be red as you were unlikely to randomly get the red ball at the start. In fact the chance is 1/100 that your first choice was right.

But if instead he randomly flings 98 balls out of the bag and they are all black then the fact that he didn't fling out the red ball by chance makes it more likely that red ball was the one you chose at the start. In effect the host has randomly selected a ball to leave in the bag and you randomly selected a ball to take out at the start. You know that

*against the odds* one of those two balls turned out to be the red one so the chance that your choice is red is 1/2