Combinations question: choose number of balls to give a desired probability of winning?

Asked Apr 01 '17 at 20:10

Active Apr 01 '17 at 20:10

Viewed 23 times

Let's say I have a lottery where each player chooses 6 unique balls.

There are 5000 players.

How do I choose the number of balls so that there's a ~95% probability of winning???

I can do this by using the following function:

function getRange(int nEntries){
    int nBalls=6;
    while(nCr(nBalls,6)<nEntries){
      nBalls=nBalls+1;
    }
    return nBalls;
}

, however this is searching rather than working it out ;( I would like to make this function more efficient as I'm on a very constrained computer and this function will be called a lot.

asked Apr 01 '17 at 20:10

Eamorr

choose, randomly, a $95$% of the different balls, then you have a probability of $95$% of winning. – Masacroso Apr 01 '17 at 20:28
$;n=15;$ is pretty close to solve $;\binom n6\approx5,000;$ , but the estimmation is by hand... – DonAntonio Apr 01 '17 at 20:40
The number of entries will change. I need to be able to change the number of balls to give 95% chance ;( – Eamorr Apr 01 '17 at 21:11

Combinations question: choose number of balls to give a desired probability of winning?

0 Answers0