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  • 33% chance
  • Door 1
  • If I pick the first door, the first door has a 33% chance of getting the car, which means the two doors I did not choose have a combined 67% chance of getting the car. 
  • Door 2
  • 67% chance
  • Door 3
  • Let's say I pick Door 1 and the host shows that Door 3 has a cow. I still know I have a 33% chance of getting the car from Door 1 and a combined 67% chance from Doors 2 and 3. However, with my new information, I know that Door 3 does not have the car. This means that Door 2 now gets the full 67% chance of getting the car.
  • Door 1
  • 33% chance
  • Door 2
  • 67% chance
  • Door 3
  • Although it might seem confusing that the combined 67% chance of both Doors 2 and 3 collapse into the percentage for only one door, when you think about it, it is not that complicated. The 67% chance is still for both doors, but we now can confirm one of the doors has a cow behind it. Therefore, the combined probability for the group only applies to one door because the other door has been "eliminated". The 67% chance no longer applies to the door that is opened. It is always better to switch.
  • Door 1
  • 33% chance
  • Door 2
  • 67% chance
  • Door 3
  • Of course I switch. If I switch, I get an additional 33% chance.
  • Most impressive. That was a very fast answer. Great job. Class, this is a mathematical genius in the making.
  • The teacher loved and praised me so much that he inspired me to be a math teacher myself and inspire even more youth.
  • Sources: https://www.youtube.com/watch?v=4Lb-6rxZxx0 https://www.youtube.com/watch?v=mhlc7peGlGg
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