Question

(1 point) Whooping cough (pertussis) is a highly contagious bacterial infection that was a major cuase of childhood deaths before the development of vaccines. About 80% 80% of unvaccinated children who are exposed to whooping cough will develop the infection, as opposed to only about 5% 5% of vaccinated children.

A group of 3 vaccinated children at a nursery school are exposed to whooping cough by playing with an infected child. What is the probability that at least one of the 3 children develop an infection?

Answer 1

Here, n = 3, p = 0.05, (1 - p) = 0.95 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 1).
P(X >= 1) = (3C1 * 0.05^1 * 0.95^2) + (3C2 * 0.05^2 * 0.95^1) + (3C3 * 0.05^3 * 0.95^0)
P(X >= 1) = 0.1354 + 0.0071 + 0.0001
P(X >= 1) = 0.1426