A forest contains 20 elk, of which 5 are captured, tagged, and then released. A certain time later, 4 of the 20 elk are captured. What is the probability that 2 of these 4 have been tagged? What assumptions are you making?
Here's my attempt. First of all, I assume that if 3 or 4 of the members of the second capture are tagged then that group still counts because technically 2 of them are tagged. It is not explicitly stated in the question that no more than 2 are allowed to be tagged. I came up with the following result:
(C(5, 2)(16, 2) + C(5, 3)C(16, 1) + C(5, 4)C(16, 0))/C(20, 4) = 91/323.
My book says that the correct answer is 70/323. Since my answer was larger I figured that perhaps the author was asking for the probability of the group only containing two tagged members instead.
C(5, 2)(16, 2)/C(20, 4) = 80/323.
Close, but not close enough. Considering my inexperience i dare not question the author so I assume I've done something wrong. However, I cannot for the life of me figure out what I might've done wrong, could someone lend me a hand please?
Edit: The sixteens should be fifteens right? Let me try that and get back to you. Yep that was it. I helped myself, but I can't give myself a like. Unacceptable!