Question

There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. A county health 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

binomial distribution formula: https://www.onlinemathlearning.com/image-files/binomial-distribution-formula.png

in this case, your n value is the # of people (83), x is 10 (since we want to know the probability for 10 people), p is 20% (or 0.20, the probability of getting the disease), q is 1 - p. plug in the appropriate quantities and evaluate.