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
The reason is quite simple.
If your initial choice was incorrect, and you switch, you have a 100% chance of getting the car.
Since the odds of your initial choice being incorrect were 2/3rds, therefore the odds of winning if you switch is *also* 2/3rds.
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