Which box will you pick?!

Started by Ho-Oh May 6th, 2009 12:01 AM
  • 645 views
  • 14 replies

Ho-Oh

used Sacred Fire!

Age 31
Female
QLD, Australia
Seen June 5th, 2022
Posted April 23rd, 2022
35,988 posts
17.5 Years
Suppose you're on a game show, and you're given the choice of three boxes: Under one box is the most amazing thing you've ever seen; under the others, someone's socks. You pick a box, say No. 1, and the host, who knows what's behind the boxes, opens another box, say No. 3, which has a sock. He then says to you, "Do you want to pick box No. 2?" Is it to your advantage to switch your choice?
lol, my wording sucked, c/ping and rewording from the example. :3

twocows

The not-so-black cat of ill omen

Age 32
Male
Michigan
Seen February 19th, 2023
Posted April 30th, 2021
4,307 posts
14.2 Years
I seem to remember this problem in my high school math courses. If you switch, you have a better chance of getting the thing you want (source).

Here are the choices:
Initially pick car
Initially pick goat 1
Initially pick goat 2

Let's assume you switch after he has eliminated the other door (he will never eliminate the door with the car behind it).
If you pick the car and then switch to the remaining door, you will lose.
If you pick goat 1 and then switch to the remaining door, you will win.
If you pick goat 2 and then switch to the remaining door, you will win.
Therefore, if you switch, the probability of winning is 2/3.

Let's assume you don't switch after he has eliminated the other door.
If you pick the car and don't switch to the remaining door, you will win.
If you pick goat 1 and don't switch to the remaining door, you will lose.
If you pick goat 2 and don't switch to the remaining door, you will lose.
Therefore, if you do not switch, the probability of winning is 1/3.
VNs are superior to anime, don't @ me

Aurafire

provider of cake

Age 32
Male
New York
Seen April 25th, 2017
Posted November 8th, 2011
5,735 posts
15 Years
Ugh, I remember seeing this in that movie 21. They asked the exact same problem in his math class, and apparently by some weird calculation, you actually have a 66.7% chance of winning if you switch choices instead of 50% if you stick with your original choice. So yeah, I'd switch I guess :D