Fishing Until the Fourth Tag
A lake contains N fish, 30 of which are tagged. Fish are caught one at a time, at random without replacement, until the fourth tagged fish appears. The fourth tagged fish is the 25th fish caught. What is the maximum likelihood estimate of N? The maximizer is unique.
Related problems & prerequisites
Worth solving first
Source: Inverse-sampling (negative hypergeometric) capture-recapture design. Statement written for AxiomIQ.