What is the probability that 10 of the 12 hens will lay eggs on a given day?

Question

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?

Answer 1

The number of eggs lain on a given day is an example of a "binomial random variable" (at least, it is given the assumptions made in this problem).

Using the mass function for a binomial random variable, we have that

p(exactly 10 out of the 12 hens will lay an egg) = C(12,10)*(0.80)¹⁰

*(0.20)²

≈0.284