I was watching Brooklyn 99 Season 4 Episode 8 around the 5 minute mark
The problem goes “There are 3 doors behind one of which is a car. You pick a door and the host, who knows where the car is, opens a different door showing nothing behind it. He asks if you want to change your answer.
Apparently the math dictates that you have better chances if you change your decision. Why? 2 doors 50/50 chance, no?
One character (Kevin) says it’s 2/3 if you switch 1/3 if you don’t. What? How? Please help.
In: Mathematics
Posting this as a top level comment in case this explanation helps anyone;
The break down in logic most people have is not realizing the way the initial condition is set up. Look at it from the first pick.
You have a 2/3 chance of picking the wrong door initially, so that is most likely what you do. Now after you pick he eliminates one of the wrong options, but you already picked based on 2/3 probability, so you likely already picked the wrong door, thus meaning that if you were to switch doors 100% of the time after given the option you will switch from a wrong door to a right door 2/3 of the time.
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