Elk Probability

Question

Twenty elk live in a forest, and 7 were tagged and released. Some time later, 5 elk were randomly caught. Assume all 20 elk were equally likely to be caught. What is the probability that exactly 2 of these 5 elk caught were previously tagged? Do NOT round.

Answer 1

7 out of 20 elk have been caught, tagged, and released

with another 13 of the 20 still untagged.

The probability that exactly 2 of another 5 captured elk

are already tagged would then be expressed as:

[5! ÷ 2! ÷ (5 − 2)!] times (7/20)² times (13/20)³.

This amounts to 10 times (49/400) times (2197/8000)

or (1076530/3200000) or 0.336415625.