3. (15 pts) Suppose there are 500 deer in a wildlife preserve. A sample of 50 de

Question

3. (15 pts) Suppose there are 500 deer in a wildlife preserve. A sample of 50 deer are caught and (ear) tagged and returned to the population. After allowing some time for the deer to "mix," a second sample of 20 deer are caught a. Write, but don't evaluate, an expression for the chance that exactly two deer are tagged in the sample of size 20. b. Write, but don't evaluate, an expression for the chance at least three deer are tagged in the sample of size 20 In many situations the total population size, 500 here, is unknown. Such a capture-recapture procedure discussed here may be used to estimate the unknown total population size.

Explanation / Answer

a) P(exactly 2 deer are tagged in sample of 20) = 50C2 * 450C18 / 500C20

NOTE: Here 50C2 = 50! / (2! * (50 - 2)!) = 50! / (2! * 48!)

b) P(at least 3 deer are tagged in sample of 20) = 1 - (P(zero are tagged) + P(1 is tagged) + P(2 are tagged)

                                                 = 1 - [450C20 / 500C20 + 50C1 * 450C19 / 500C20 + 50C2 * 450C18 / 500C20]

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