Suppose that in a certain population of lizards, the probability of the birth of a male is 0.6.Assume that the sex of each individual is independently determined.What is the probability that a clutch of three will have exactly two females? (Note that there are three ways to arrive at this outcome when calculating the probabilities of each egg's sex.)
A) 0.096
B) 0.125
C) 0.196
D) 0.288
E) 0.375

Question

Quizplus · Accepted Answer

The probability of having exactly two females in a clutch of three, given that the probability of a male birth is 0.6 (thus, female birth is 0.4), can be calculated using the binomial probability formula. The formula for exactly k successes (female births) in n trials (eggs in the clutch) is: C(n, k) * p^k * (1-p)^(n-k), where C(n, k) is the combination of n items taken k at a time, and p is the probability of success (female birth). Here, n=3, k=2, and p=0.4. The calculation is: 3C2 * (0.4)^2 * (0.6)^1 = 3 * 0.16 * 0.6 = 0.288.

Suppose That in a Certain Population of Lizards, the Probability