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Monty hall problem

Monty hall problem

Monty hall problem was named after the American game show Lets make a deal hosted by Monty hall. Its a brain teaser puzzle.

Here is the puzzle,

There will be three doors. Behind one of the door is the car and behind other two doors are the goats.

The host will ask the contestant to pick one of the door. Consider it as Door 1. It will remain unopened.

Host knows what is behind the three doors. So, he opens one of the unpicked door, consider it as door 3. Host always opens the door with the goat. Now the host gives the open choice to stick with the door 1 or to pick the Door 2.

What is the best choice now for the contestant. Should he stick to his pick or should he change his choice.

Math suggests that its always good to change the door. Why?

Contestant who switch every time will lose only when the door they selected initially have car behind it.

Hence we can say that chance of winning the game on the first move is 1/3 and the chance of losing the game when you change the door is also 1/3

Contestant who change the door every time have 2/3 chance of winning the car.

So if you stay back with the same door, your chance of winning the car is 1/3 and when you switch your chance of winning the car is 2/3

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