I understand that the name is a bit strange. But this is a statistic problem that I'm trying to figure out, but I'm at a dead end. (No no, this is not homework, see Bottom for a real explanation)
The premise is simple. You have N buckets. Each bucket may contain H balls. None of the buckets are full. You have D balls already in the buckets, but you don’t know where the eggs are (you forgot!) You pick a bucket at random to add 1 ball. What is the likelihood that this bucket will be full.
Some examples of possible diagrams, with N = 4, H = 3, D = 4. Each case is simply a hypothetical arrangement of balls. for one of many cases.
Scenario 1: 1 bucket could be filled.
| | | | |
+ - + - + - + - +
| B | | | |
+ - + - + - + - +
| B | B | | B |
+ - + - + - + - +
Scenario 2: 2 buckets could be filled.
| | | | |
+ - + - + - + - +
| | B | B | |
+ - + - + - + - +
| | B | B | |
+ - + - + - + - +
Scenario 3: 0 buckets could be filled.
| | | | |
+ - + - + - + - +
| | | | |
+ - + - + - + - +
| B | B | B | B |
+ - + - + - + - +
The problem is that I need a general-purpose equation in the form P = f (N, H, D)
, . - . , . . . , , . , f (N, H, D) % , ( HP ). , N 1 D H.
. , VAST VAST, . , .