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.)