Let X be the random variablenumber of tagged trout in the second sample.

a) .

More generally, if m trout are caught and returned after they are tagged, and k trout are later caught and found to contain x tagged trout:

.

b) The best estimate of n is the integer value of n that maximises Pr(X = 7).

Using technology is the easiest way of finding this value (although it's not difficult to do by hand if you use the right approach).