The Monty Hall Game Show Problem.
In a game show there are 3 doors.Behind each of two doors is a Goat!
Behind one of the doors is a brand new Car!
The host asks you to select one door, but not open it yet.
The host then goes over to the other two doors and opens one of them to reveal a Goat.
He then asks you if you want to swap your door with the other unopened door.
Should you Swap or Stick with your original choice?
Many people will intuitively say that it doesn't make any difference and that the chance either way is 50-50!
However, the answer is that you should swap, as it gives you twice the chance of winning the car!
Think about it this way.
On your first choice you have 1/3 chance to win the Car, and you have 2/3 chance of getting a goat.
If you're sitting on the goat and the host choses the other goat then only the car remains so when you swap you win the car!
It's really very simple, but quite counter intuitive. Even the great number theorist Paul Erdős didn't believe this result at first along with many other academics.
The diagram below does the formal math probabilities which seems more confusing than the simple explanation above! (simple is always better)
The tree diagram assumes that the Player has initially chosen Door 1.
More in depth explanations with good diagrams:
http://mathforum.org/mathimages/index.php/The_Monty_Hall_Problem
https://en.wikipedia.org/wiki/Monty_Hall_problem
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