A farmer decides to estimate health of the fish population he has in one of his dams. He
catches 850 fish on a particular day, marks them with a tag and returns them to the water. A
week later he catches 100 fish. The number of tagged fish in this sample is 35. When the
farmer marks the fish, he marks those fish that are smaller than the minimum size for
harvesting with a green dot. However, it is difficult to accurately measure a wriggling fish.
The farmer estimates that the probability of correctly marking an undersized fish as
undersized is 0.85, and the probability of marking a fish as undersized that is, in fact, not
undersized is 0.25. It is estimated that 0.004 of the population will be undersized for
harvest. Let
A ⇔ is undersized,
B ⇔ marked as undersized