You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats, if you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open, what should you do?

Hint: It is not 1/2 as you would first think.

The answer is 2/3, and here is the proof.

Call the doors x, y and z

Cx is the event that the car is behind door x

Cy is the event that the car is behind door y

Cz is the event that the car is behind door z

Hx is the presenter opening door x with the goat

Hy is the presenter opening door y with the goat

Hz is the presenter opening door z with the goat

Say you chose door x, the following formula shows the chance of getting the car.

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You are on a game show and there are three doors. The presenter tells you that behind one of doors there is a car and behind the other two are goats, if you pick the car you win it. After you have picked a door the presenter opens a different door with a goat behind it, he then gives you the chance to change what door you open, what should you do?

Hint: It is not 1/2 as you would first think.

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