If 50 of the subjects transported by helicopter are randomly selected without​ replacement, what is the probability that none of them left the treatment center against medical​ advice?

Question

In a study of helicopter usage and patient​ survival, among the

40,674 patients transported by​ helicopter, 201 of them left the treatment center against medical​ advice, and the other 40,473 did not leave against medical advice.

Answer 1

The exact probability is ₄₀₄₇₃C₅₀ / ₄₀₆₇₄C_50.

_{For numbers this big you can probably get a good approximation by using the binomial or by using Stirling's approximation to the factorial.}