The probability that a mature hen will lay an egg on a given day is 0.80. Hannah has 12 hens. What is the probability that 10 of the 12 hens will lay eggs on a given day?

Use the binomial probability for exactly 10 hens laying eggs: choose which 10 hens lay, then multiply by the probabilities that those 10 lay and the other 2 do not. This gives C(12,10) × 0.80^10 × 0.20^2 = 66 × 0.80^10 × 0.20^2 ≈ 0.283. Rounded to the choices, the probability is 0.28, choice D.

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