Questions: In a study of helicopter usage and patient survival, among the 47,773 patients transported by helicopter, 260 of them left the treatment center against medical advice, and the other 47,513 did not leave against medical advice. If 40 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?

Solution Steps

The probability for the first draw is given by \(\frac{N-K}{N}\), where \(N\) is the total population and \(K\) is the number of individuals with the specific attribute. In this case, it is \(\frac{47513}{47773}\).

For each subsequent draw, the population decreases by 1, as does the number of individuals without the specific attribute (if one was selected). Thus, for the second draw, the probability becomes \(\frac{N-K-1}{N-1}\), and so on. This adjustment continues for each of the \(n\) draws.

The overall probability of selecting \(n\) individuals without the specific attribute is the product of the probabilities of each draw. This can be represented as \(\prod_{i=0}^{n-1} \frac{N-K-i}{N-i}\). For our parameters, this calculation gives us a probability of 0.804.

Final Answer: