>>12291726Yes, it’s related to monty hall.
It‘s way clearer when you think about larger numbers:
>Monty Hall:Imaging one million doors.
You pick one random door.
All doors exept one gets opened.
Should you switch?
Yes, because in the first try you only had a chance of 1 to 1,000,000.
>golden ballsFirst setting:
Imagine three boxes:
-Box 1 has one million golden balls
-Box 2 has one million silver balls
-Box 3 has one golden ball and 999,999 silver balls
You grab one ball, what are the chances the next one is golden?
Well, the chances that you picked the one golden ball among all those silver balls is tiny, to be exact:
1 to 1,000,000
So the chances that the next one from is golden is 1,000,000 to 1.
How is it related to monty hall?
We change the setting slightly:
The mixed box has 5 golden balls and 999,995 silver balls.
New question:
If you picked 4 golden balls from one box, what are the chances, the next one will be golden?
The possibility to get one golden ball from on the mixed box is:
5:1,000,000
There are „n choose k“ possible combinations im this scenario, so the possibility to get 5 golden balls is „1,000,000 over 5“, which really really small.
Even if we look at the problem in terms of conditional probability, the outcome doesn’t really change.
In layman’s terms:
With each golden ball we draw, we can be more certain that we are in the „golden balls only box“.
This is like monty hall, where each open door makes it more certain what is hidden behind the doors left closed.
