Question

Seventeen people have been exposed to a particular disease. each one independently has a 40% chance of contracting the disease. a hospital has the capacity to handle 10 cases of the disease. what is the probability that the hospital capacity will be exceeded

Answer 1

We can rewrite the problem like this:
"What is the probability that more than 10 people out of 70 contract the disease".
Each person has a probability to contract the disease of 0.4
So, we will compute the probability that 10 person contract the disease, of 11, or 12 ... and so one. So our formula will be written like this:
$0.4^{10}0.6^{60}C_{70}^{10}+...+0.4^{70}C_{70}^{70}=1-(0.4^{0}0.6^{70}C_{70}^{0}+0.4^{1}0.6^{69}C_{70}^{1}\\+0.4^{2}0.6^{68}C_{70}^{2}+0.4^{3}0.6^{67}C_{70}^{3}+0.4^{4}0.6^{66}C_{70}^{4}\\+0.4^{5}0.6^{65}C_{70}^{5}+0.4^{6}0.6^{64}C_{70}^{6}+0.4^{7}0.6^{63}C_{70}^{7}\\+0.4^{8}0.6^{62}C_{70}^{8}+0.4^{9}0.6^{61}C_{70}^{9})\\=$ 
It remains to use calculator and evaluate all the above expression.