Question

Suppose that 3% of the students at a particular college have the H1N1 influenza virus.

If a student gets together with 30 other students over a period of time, what is the theoretical probability that at least one of those 30 students has the H1N1 influenza virus? Show as a percentage with 3 decimal places.

Answer 1

n = 30

p = 0.03

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X > 1) = 1 - P(X < 1)

               = 1 - (P(X = 0))

               = 1 - (30C0 * (0.03)^0 * (0.97)^30)

              = 1 - 0.40101

              = 0.59899 = 59.899%