9th Puzzle Answer

You should accept his offer and choose the other door, by doing so you double your odds of winning the car.
No, I'm not crazy, the reason is as follows:

  1. The probability that the car is behind your original selection is 1/3, which means the probability that it is behind one of the other 2 doors is 2/3.
  2. The 2 doors that you have originally rejected share an equal 50/50 chance of their common 2/3 probalility while the show compere leaves the doors shut, when he opens one of the doors, he provides you with additional information.
  3. This additional information is that while the probability of the car of being behind one of those 2 doors is still 2/3, the probability that it is behind the now open door is obviously 0%, which means the probability of being behind the other one is 100% of 2/3.

You still don't believe me, ok let's assume your original pick was door # 1. Here are the 3 possibilities:

         Door 1    Door 2    Door 3

case 1    car        x         x             compere opens either door 2 or 3,
                                             if you change your mind, you lose!

case 2     x        car        x             compere open door 3,
                                             if you change your mind, you win!

case 3     x         x        car            compere opens door 2,
                                             if you change your mind, you win!
If you change your mind you have 2/3 chances of winning, if you don't you only have 1/3.

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