Number of balls in population, from samples Let's say there are $n$ balls in a box, each either blue or red. We randomly picked up 5 balls - we got 3 red and 2 blue balls.
And we replaced all the balls, shuffled for a bit, picked another 20 balls, and got 15 blue balls and 5 red balls. We replaced and shuffled all the balls, picked 50 balls randomly, and got 50 blue balls.
A) We met the person who placed balls into the box before we did all the sampling. He doesn't remember how many balls are in the box, but he remembers placing blue balls first before placing red balls. This means when we picked the first 5 balls, we will have higher chance to get red balls. Do you think he was correct?
B) How many total balls do you think he has? (likely estimate?)
Feel free to change numbers to make it possible to arrive at a fixed solution.

The total number of balls in the urn $n$ would be identifiable from the amount of underdispersion in these hypergeometrically distributed counts.  But for the particular data set above there is some overdispersion which sends the maximum likelihood estimate of $n$ off to infinity.  This is illustrated by the following code which computes and plots the likelihood as a function of the number of blue and red balls in the urn.
x <- c(2, 15, 50)
n <- c(5, 20, 50)
l <- function(par,x,n) {
  sum(dhyper(x, par[1], par[2], n,log=TRUE))# - log(sum(par))
}
blue <- 50:400
red <- 5:40
lmatrix <- matrix(NA, nrow=length(blue), ncol=length(red))
for (i in seq_along(blue)) for (j in seq_along(red))
  lmatrix[i,j] <- l(c(blue[i],red[j]),x,n)
contour(blue,red,lmatrix, nlevels=100, xlab="no. of blue balls", ylab="no. of red balls")


