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
It’s easier to explain backwards. When you pick one option out of three there is a 2/3 chance that the correct answer was behind the other doors. You picked one there were two left. The odds say that one of the ones you didn’t pick has the prize. If you could pick 2 doors instead of one you would have a 2/3 shot of winning. However if you pick 2 doors you know one has to be empty. In this scenario it is like picking 2 doors and the host tells you which one is empty and then let’s you have the last one.
Let’s do the experiment:
Take 3 cups and 1 ping pong ball. Line the cups up in a row. Place the ball under cup 2. You switch cups every time offered by the host.
First experiment you pick cup 1. The ball is under cup 2. The host shows that cup 3 is empty and asks if you want to switch to cup 2. You do and win.
Second experiment you pick cup 2. The ball was under this cup. Host shows you cup 3 is empty and asks if you want to switch to cup 1
You do and lose.
Third experiment you pick cup 3. The ball is under cup 2. Host shows you cup 1 is empty and asks if you want to switch to cup 2. You do and win.
You win 2 out of 3.
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