Calculate the probability that 30 of more females are captured (out of 50)

Question

The Wisconsin deer population is monitored for Chronic Wasting Disease (a disease caused by a prion). Deer are captured, measurements are taken, and then the animals are released. It is assumed here that male and female deer are in equal proportion in the wild and are equally likely to be captured.

Answer 1

Probability of selecting a female=0.5.

Number of trials=50.

Probability of 30 or more females using binomial distribution is 10.13% (from tables).

Based on (p+q)⁵⁰=1 where p=q=0.5. The same probability for selecting no more than 20 males, sum the terms of the series to get cumulative probability. It’s assumed that each deer in turn is released back into the community, or that all deer are collected and then all are released following monitoring arrangements. (Otherwise, hypergeometric distribution would apply as each deer was captured and held, so the community was gradually depleted.)

Comments

Probability is so difficult. My little brain hurts when I see a probability question. I want to give you a like for this answer but I cannot as I don't have administrative powers as you do.

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I sometimes struggle with probability, too. Thank you for your kind intentions.