this post was submitted on 11 Feb 2024
70 points (96.1% liked)
Showerthoughts
29793 readers
926 users here now
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. A showerthought should offer a unique perspective on an ordinary part of life.
Rules
- All posts must be showerthoughts
- The entire showerthought must be in the title
- Avoid politics
- 3.1) NEW RULE as of 5 Nov 2024, trying it out
- 3.2) Political posts often end up being circle jerks (not offering unique perspective) or enflaming (too much work for mods).
- 3.3) Try c/politicaldiscussion, volunteer as a mod here, or start your own community.
- Posts must be original/unique
- Adhere to Lemmy's Code of Conduct
founded 1 year ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Now you have 2 choices: the door you chose, or the only other door left. One has a goat and one has a car. That's fifty-fifty.
In your explanation, the door originally had a 1% chance, but after showing 98 goats, it has a 50% chance.
No. Taking it to the extreme with 100 doors, your first pick was a 1% chance to get the car. The host then shows you 98 other doors that all have goats.
What’s more likely? That you picked the right door when it was 100:1? Or that the other door is the one with the car?
There are 2 choices so they are equally likely
They’re really not.
The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
The host's intentions are irrelevant. Numerically, there are only two choices. That makes it fifty-fifty.
You think that even in the hundred-door case? Test it. Hell, even test it in the 3 door case. It is empirically not 50%.
If the host had an even chance to show you either door, you'd be right, but since the host always shows you a goat, the two events (picking a door and choosing whether to switch) are no longer independent, since if you pick a goat it forces the host to pick the other goat.