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 male?
To calculate the probability that no more than two eggs are male, we need to calculate the probability of choosing 0, 1, or 2 male eggs and then add these probabilities together.
Let's denote the event of choosing a female egg as F and the event of choosing a male egg as M.
P(no male eggs) = P(FFF) = 0.6 * 0.6 * 0.6 = 0.216
P(1 male egg) = P(FMF or FMF or MFF) = 3 * 0.6 * 0.4 * 0.6 = 0.432
P(2 male eggs) = P(MMF or MFM or FMM) = 3 * 0.4 * 0.4 * 0.6 = 0.288
Therefore, the total probability that no more than two eggs are male is:
P(no more than two male eggs) = P(0 male eggs) + P(1 male egg) + P(2 male eggs)
P(no more than two male eggs) = 0.216 + 0.432 + 0.288
P(no more than two male eggs) = 0.936
Therefore, the probability that no more than two eggs are male is 0.936 or 93.6%.