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?
This is a binomial probability question.
The probability that any inoculated person will get sick is 0.2
The probability that any inoculated person will not get sick is 1-0.2 = 0.8
The probability that the first 10 people get sick and the next 73 people do not is 0.2 10 * 0.8 73
Trouble is, it might not be the first 10 people that get sick, it could be some other combination of 10 people that get sick, so a formula is needed to work out how many possible ways 10 people can be chosen from a total of 83 people. That formula is 83C 10
so the answer will be
83C 10 * 0.2 10 * 0.8 73
This can be done on your calculator.
+118651 
