Monty hall problem

 https://m.youtube.com/watch?v=9UBMEww7XLU

 

 

This seems unintuitive. You pick between 3 doors. 1 door is right. Now before showing you your door, one of the other 2 doors is opened showing a wrong result. Then you are asked, do you want to switch your door for the other unopened door? If you switch doors you have a 2/3 chance of being right. Why isn't it 1/2 chance?

Well, your original pick had a 1/3 chance. So, most of the time you guess wrong. They eliminated one door. If you always switch, you are changing from your 1/3 guess, which switches you to a 2/3 chance. This only works because they eliminated a wrong door first.

Also, if your original guess was right, then switching will lose, but you only lose 1/3 of the time.