### 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 ?**

See Answer

**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.

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

Larry Crain says

This thing is so silly that I cannot believe it was discussed so much.Changing doors has 0% advantage. If you do not agree then try the game with two players who select different doors.

Smit says

that is wrong. there are 3 doors so probability is 33.33 for each door. say i choose door 1. door 3 has a goat. so probability of my door becomes 66.66 n the other 1 is 33.33. so i shud stay with the same door.