Finding Your Birthmate

You want to find someone whose birthday matches yours. What is the least number of strangers whose birthdays you need to ask about to have a 50-50 chance? ¹

The problem can be modeled as a negative binomial with parameters $r = 1$ and $p = 1/365$, hence the PMF is given by $\left(\frac{N-r}{N}\right)^\frac{1}{p} p$.

Since we want to find the number that gives us a 50-50 chance, we need to calculate the inverse CDF of the negative binomial and find the value for $0.5$. The CDF of the negative binomial is given by:

I still don’t know how to compute the inverse of this CDF, but a numerical approximation gives us 252. In Maxima, one can use: quantile_negative_binomial(0.5, 1, 1/365);