Actually the point is only the number matchings on the lottery using just 3 player numbers.
This is a conditional probability problem.
I experimented on matching all numbers between ABCD;EE and ABCD;EE
Hypothetic (calculated) probability: 1/1260
Real probability: ~1.75/1260...
What is the probability of the player matching exactly 3 numbers from a 10 number lottery (0...9) w/o repetition, given the conditions:
- player and lottery pick 6 numbers;
- player always has a repeated number;
- lottery always has a repeated number.
Well, that wiki bit was inspiring, even if it that formula I posted is wrong for this problem because it's for no replacement balls.
I should've posted this one instead perhaps:
The general formula for B matching balls in a N choose K lottery with one bonus ball from a separate pool of P...
I didn't calculate the probability right in the last part, it's 5040/56700, which is 0.0(8), or 4/45.
Where did I go wrong:
C(5,2)C(10-5,0)/C(10,2)=10/45 for the hipergeometric part, then, because the repeated unit can only be one of those first two that matched, it has 2/10...
Problem solved experimentally, but need to find an elegant combinatorial formula for approximating the result instead.
Also need verification of the solution below.
Problem data is:
sample space is numbers from 0 to 9
lottery picks 6 numbers, but only 2 are distinct (Example: 111444)...
Have an example:
the sample space is 0..9
row 1 can pick 6 numbers out of which 2 are repeated
row 2 can pick 6 numbers out of which 3 by 3 are repeated
I want to know what is the real probability that row 1 will match with 2 distinct numbers numbers row 2, and a repeated number...