The Monty Hall problem is an interesting mathematical puzzle that brings to fore a non-intuitive nature of probability. It is named after Monty Hall, the host of the American television game show "Let's Make a Deal".
Let's assume that you are a contestant on a game show. There are three doors in front of you: behind one door is a car, behind the other two are goats. You pick a door, say door 1. Being familiar with what is behind every door, the presenter pulls up door 3, and a goat comes out. Then, you are asked whether you want to stay with the same decision (Door 1) or go to the other closed door (Door 2). What is the best way to increase your chances of winning the car?
Intuitively, it may seem like your odds are 50:50. Regardless of whether you switch or stay, it is still 50%. Contrary to this belief, this is not the case. If you stick to your first choice, you have a 1/3 chance of winning the car, but if you switch, your chances increase to 2/3.
The reason for this is as follows: If your first selection is the car, you have a 1/3 chance of having chosen the car and a 2/3 chance of the car being behind one of the other two doors. A host who exhibits a goat and leaves the door open will not affect the probabilities. There is still a 1/3 chance that the car is behind your first choice, and a 2/3 chance that it is behind one of the other doors. But now one of these doors is gone, the 2/3 probability changes in favor of the door that is still closed.
This shows us that our intuition might be different than the mathematical aspects, happy problem solving!
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