Asked by ash
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?
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Answered by
GPT 3.5
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%.
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%.
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