1. To estimate the number N of goldsh in a pond, 'r = 25 sh were caught, tagged and released. Later, a second random sample1 of n = 20 sh were caught and 5 sh in this sample were tagged. a. Give an expression in terms of N for the probability that 5 sh in the second sample are tagged. Hints, to encourage independent work: . How many diiferent samples 20 sh can be formed from all N in the pond? (Each sample is equally likely) . How many of these samples have 5 tagged shes? b. One way to estimate N is to pick the value that makes the probability in part (a) as large as possible. Why does this idea make sense? Please explain briey, but in complete sentences. (Note: we want to evaluate your ability to think critically and also your statistical sense. So please do not ask anyone for help with this question. We want to know what you think. )