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
There are a ton of resources on the web or youtube that explains this which will go through the steps of reasoning this out. Much better than a wall of text.
Monty Hall illustrates a very important point about the nature of new information and how it updates your prior probabilities. For example:
You fall down some stairs and hurt your right foot and believe there is a 25% chance it is broken. You go to a clinic and they examine your left foot and say “left foot isn’t broken”. Does this make it more or less likely that your right foot is broken?
Now in the same situation, the clinic tests your right foot and say “it isn’t a sprain”. Given that your foot still hurts, is it now more or less likely that it is broken?
Monty Hall is NOT acting randomly. This is the thing that needs to be understood. Monty Hall cannot open the door the contestant chooses and he cannot open the door with the car behind it. The information he reveals by opening one door isn’t giving you EQUAL information about what lies behind the remaining closed doors.
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