Question

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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

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%.