Final answer:
To find the probabilities of the number of male and female wolves in a random sample before 1918, use the binomial probability formula. For the period from 1918 to the present, use the same formula with updated values. The probabilities can then be calculated based on the desired number of males or females.
Step-by-step explanation:
To find the probability that 8 or more wolves were male before 1918, we can use the binomial probability formula. The probability of getting exactly k successes in n trials, with a probability p of success, is given by the formula P(X=k) = nCk * p^k * (1-p)^(n-k), where nCk represents the combination of n things taken k at a time.
a) P(8 or more males) = P(X=8) + P(X=9) + P(X=10) + P(X=11)
To find the probability that 8 or more wolves were female before 1918, we can subtract the probability of having 7 or fewer males from 1:
b) P(8 or more females) = 1 - P(7 or fewer males)
To find the probability that fewer than 5 wolves were female before 1918, we can calculate the probability of having 4 or fewer females:
c) P(fewer than 5 females) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)
For the period from 1918 to the present, the probabilities can be calculated using the same formulas, but with updated values for p (probability of a male wolf) and n (total number of wolves).