Re:Your iPhone just got less secure. Blame the FBI
by jinfiesto on Wednesday March 30, 2016 @01:58PM
(#11391455)
From the initial setup you have a 1/3 chance of choosing the correct door and a 2/3 chance of choosing the wrong door.
The key to this problem is the behavior of the game host as he will never reveal the door with the car. So, after he reveals the contents of one of the doors, if you choose not to switch, you still only have a 1/3 chance of having chosen the door with the car.
On the other hand, if you choose to switch, 2/3 of the time you will have chosen incorrectly initially, and under the switching strategy, those 2/3ds of the time you are guaranteed to win the car. Hence, you have a 2/3ds chance of winning under the switching strategy, vs a 1/3d chance of winning under the "staying" strategy.
The key to this problem is the behavior of the game host as he will never reveal the door with the car. So, after he reveals the contents of one of the doors, if you choose not to switch, you still only have a 1/3 chance of having chosen the door with the car.
On the other hand, if you choose to switch, 2/3 of the time you will have chosen incorrectly initially, and under the switching strategy, those 2/3ds of the time you are guaranteed to win the car. Hence, you have a 2/3ds chance of winning under the switching strategy, vs a 1/3d chance of winning under the "staying" strategy.
Hope this clarifies things.