Question

There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. A county healthy office inoculates 83 people. What is the probability that exactly 10 of them will get the disease at some point in their lives?

Answer 1

Let
`X` be a random variable denoting the number of inoculated people in a population of size
`n` that contract this disease.
`X` is said to be binomially distributed with probability
`p=0.2`, or
`X\sim\mathcal B(83,0.2)`.

So the probability that exactly 10 of 83 people get the disease, despite inoculation against it, is


`\mathbb P(X=10)=\dbinom{83}{10}0.2^(10)(1-0.2)^(83-10)\approx0.0209842`