Population studies in biology and ecology often tag and release animals in order
ID: 3059995 • Letter: P
Question
Population studies in biology and ecology often tag and release animals in order to study the distribution, roaming habits, and other characteristics of the species. Suppose ten animals of a species thought near extinction in a region are caught, tagged, and released. After a long enough period of time for these ten to mix in with the rest of the population, a random sample of 15 of this species is caught. If there are actually 30 of these creatures in the population:
a) What is the probability that exactly 5 of the 15 animals captured the second time have tags?
b) What is the expected number of tagged animals in a sample of 15?
*Note: Solve without using Minitab or some other computer software
Explanation / Answer
a) P(exactly 5 of the 15 anmals captured the second time have tags) = 10C5 * 20C10/30C15 = 0.3
b) P(one animal of the 15 animals captured the second time have tags) = 10C1 * 20C14/30C15 = 0.0025
Expected no of tagged animals in a sample of 15 = 15 * 0.0025 = 0.0375