3 ms·
> After a large number of picks, what is the behavior of the proportion of red balls in the urn Isn’t the more enticing question how strong the bias towards th
by theK 3y ago
> After a large number of picks, what is the behavior of the proportion of red balls in the urn
Isn’t the more enticing question how strong the bias towards the first picked Color is?
- deleted 3y ago[deleted]
- kgwgk 3y agoThe expected terminal fraction is always equal to the current fraction. (Or is it?)
- inimino 3y agoYes, it is.
- fjfaase 3y agoThe rather boring answer is 2/3. Logic seems to indicate that it will be a linear distribution where the change for only balls of the first picked Color is maximum and only balls of the other Color is zero, because it is no longer possible to only pick balls of the other Color. It must be linear because it needs to be symmetric and lead to a uniform distribution if added together. After two picks, you have three cases. If you picked two different colored balls, the distribution should be a uniform distribution again, just like the initial state. The two other distribution should mirror eachother, and thus be linear again. Maybe that something interesting happens with three picks. Or maybe, you always end up with linear distributions with tilted slopes. In that case it is rather boring.
- fjfaase 3y agoI am mistaken. After two picks, the case with two of the same Color does not result in a linear distribution. You can easily check this by modifying the code.