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By far the most popular way to measure the size of a population is called the Mark and Recapture Technique. This technique is commonly used to estimate population sizes before fishing or hunting seasons.

The mark and recapture method involves marking a number of individuals in a natural population, returning them to that population, and recapturing some of them as a basis for estimating the size of the population. It is based on the principle that if a proportion of the population was marked in some way, returned to the original population and then, after complete mixing, a second sample was taken, the proportion of marked individuals in the second sample would be the same as was marked initially in the total population. That is, $$\frac{R(\text{marked recaptures})}{T(\text{total in second sample})} = \frac{M(\text{marked initially})}{ N(\text{total pop.size})}$$

Questions

1. Before the annual hunting, Robert, a hunting manager has to estimate the population of deer in his hunting area. He is allowed to kill a quota of 10% of it to preserve the wildlife. He decided to use the Mark and Recapture Technique. He captured 15 deer that he marked with red strips. The day after among the 12 deer he captured, 3 were marked. Robert told his partners that after the hunting season, they could kill a total of 10 deer. Do you agree with him?
2. Explain in which case (conditions or situations) you think this method is reliable and useful.