Suppose that 20% of the students in a college are smokers. A sample of 10 students is randomly selected from this college. What is the probability that at least 3 students in this sample are smokers?

Answer 1

s = smoker ... p(s) = .20

n = non-smoker ... p(n) = .80

this is a binomial probability ... p(s) + p(n) = 1

(n + s)^10 = n^10 + 10 n^9 s + 45 n^8 s^2 + 120 n^7 s^3 + ... + s^10

the probability is one, minus the sum of the 1st four terms
... 1 - [.8^10 + (10 * .8^9 * .2) + (45 * .8^8 * .2^2) + (120 * .8^7 * .2^3)]