3 doors 2 goats and a car problem

Problem Statement

Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1.

Now the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to switch and pick door No. 2?”

What should you do? Would you will with your current choice (door no. 1) or should you pick the door no. 2 ?
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You first though will be to stay, as it has worked out pretty well so far and since there are only two doors, there are fifty-fifty chances of winning the car.
But
Its not right, The best strategy to wins the car is to switch every time as from the below image, if you stay you win one in three times if you switch you win two in three times.

3 doors 2 goats and a car solution

You might still be thinking that there are fifty-fifty chances of winning the game, that is right only when host did not know what was behind the 3rd door, as he knew it already your probability of winning the car will be more when you switch.

Reference: http://www.businessinsider.com/the-most-controversial-math-problems-2013-3#-2