Question

10. (Blitzstein, 1.29, mod) American kestrels live in More Mesa near your professor's house. Sup- pose that there are 100 birds, of which a random sample of size 20 your professor has captured and tagged ("simple random sample means that all (20) sets of 20 birds are equally likely). The captured birds are returned to the population, and then a new sample is drawn, this time with size 10. This is an important method that is used in ecology, known as capture-recapture. What is the probability that exactly 3 of the 10 birds in the new sample were previously tagged? (Assume that a bird that was captured before doesn't become more or less likely to be captured again.)

Answer 1