A very classical (textbook) question on the Riddler on inferring the contents of an urn from an Hypergeometric experiment:

You have an urn with an equal number N of red balls and white balls, but you have no information about what N might be. You draw n=19 balls at random, without replacement, and you get 8 red balls and 11 white balls. What is your best guess for the original number of balls (red and white) in the urn?

With therefore a likelihood given by

leading to a simple posterior derivation when choosing a 1/RW improper prior. That can be computed for a range of integer values of R and W:

L=function(R,W)lfactorial(R)+lfactorial(W)+
    lfactorial(R+W-19)-lfactorial(R-8)-
    lfactorial(W-11)-lfactorial(R+W)

and produces a posterior mean of 59.27 for R and of 120.51 for W. And to the above surface for the log-likelihood. Which is unsurprisingly maximal at (8,11).