Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?"
Is it to your advantage to switch your choice?
|No, it's advantageous to keep your original answer.:||3 (10.0%)|
|Yes, it's advantageous to change your original answer.:||12 (40.0%)|
|Changing the answer does not change your odds of winning the car:||13 (43.3%)|
|Goat is delicious and I already own a car, so it's to my advantage to win the goat. Thus, I choose (answer below):||2 (6.7%)|
Now once you've answered, look up the answer online (and go make me a meal if you chose the goat).
My question is, if we mix it up...
Imagine, for example, that there are not three doors but 300 doors. There’s still just one good prize, with the rest being goats (the bad prize).
So you pick a door—say number #274. There’s a 1/300 chance you’re right. This needs to be emphasized: you’re almost certainly wrong. Then the game show host opens 298 of the remaining doors: 1, 2, 3, and so on. He skips door #59 and your door, #274. Every open door shows a goat. Should you switch?
The answer is the same as the first part - but I'd like, if possible, for someone to explain the logic behind it to me. I did some rough pen and paper sketches for it, but I suck at these. What is the probability if you switch, and what is the probability if you stay? I think it's 1/300 if you stay, and 299/300 if you switch... is that right?
TL;DR: Locke sucks at probability visualization. And yesterday was my birthday