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 key thing is that the host knows which door has the car.
Imagine a more extreme case. There are 100 doors with a car behind 1 of them. You pick door 7. The host reveals the goat behind every door except door 7 and door 38. Suddenly, door 38 looks suspiciously appealing…
You had a 1% chance of getting the right door. This means there’s a 99% chance that door 38 is the right one.
Again, the trick is that the host knows the right door. If the host didn’t, then most of the time the host would accidentally reveal where the car was. It’s the *host’s* knowledge that changes the odds.
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