Suppose that at a particular chicken hatchery, 60% of the eggs are female. You randomly choose 3 eggs. Assume the gender of each egg is independent of the other eggs.What is the probability that no more than two eggs are female?
To find the probability that no more than two eggs are female, we need to find the probability of getting 0 female eggs, 1 female egg, or 2 female eggs.
The probability of getting 0 female eggs:
P(0 female eggs) = (0.4)^3 = 0.064
The probability of getting 1 female egg:
P(1 female egg) = 3C1 * (0.6)^1 * (0.4)^2 = 0.288
The probability of getting 2 female eggs:
P(2 female eggs) = 3C2 * (0.6)^2 * (0.4)^1 = 0.432
Therefore, the total probability of getting no more than two eggs is female is:
P(0 female eggs) + P(1 female egg) + P(2 female eggs) = 0.064 + 0.288 + 0.432 = 0.784
So, the probability that no more than two eggs are female is 0.784 or 78.4%.