The Three Doors Probability Puzzle

The three door probability problem is infamous in the world of statistics and probability. It is associated with the long-running show Let's Make a Deal which was hosted by Monty Hall.

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Amy, a game show contestant, is presented with three doors. She is told that $1K ($1,000) is behind one of the doors and nothing is behind the other two. Amy can choose one door and if it is the correct door, then she will win the thousand dollars.

   

Amy selects door 1, which is then marked with a small "x".  The game show host, knowing which door has $1K behind it, then opens up door 2 to show Amy that nothing is behind that door.  (In this game show, the host always opens up another door which does not have the winning prize behind it.)  Things now look like this:

   

The host now offers Amy the opportunity to switch to door 3 or to stay with her original choice.

Click the link below that would be your answer to what Amy should do:

Stay with the door she had originally chosen

Switch doors

It does not make a difference