# 3 ways to understand the monty hall problem.

3 gates are shown to contestant, 2 contains poop/goat and 1 contain the money. Contestant is asked to choose one of them, they get what the gate is hiding.

Contestant chooses one gate, now 1 gate have poop/goat and another one have money. Contestant can now switch if they want. Most of the time the contestant keep their selection as by this time they have realized that they have a 50-50 chance of winning and most of the time contestant looses.

## 1. Initially their is 1/3 chance of selecting a money gate and 2/3 of poop gate, higher chance of selecting poop gate than money gate.

If perform switching then we would have higher chance i.e. 2/3 to turn towards money gate.

## 2. Writing out all the probabilities.

No switch

1P -> 2P opens -> No switch -> Poop

2P -> 1P opens -> No switch -> Poop

1M -> 1P opens -> No switch -> Win

Switch

1P -> 2P opens -> Switch -> Money

2P -> 1P opens -> Switch -> Money

1M -> 1P opens -> Switch -> Poop

Their is 2/3 chance of winning in case of switching.

Did I skipped?

1M -> 2P opens -> Switch -> Poop.

## 3. We need to find the way to select a majority.

If we select out the poop their is 2/3 chance of us selecting poop in first instance. Without switching, we would be taking out the poop but with switching we could take out the poop.

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