Question

in a study of helicopter usage and patient​ survival, among the patients transported by​ helicopter, of them left the treatment center against medical​ advice, and the other did not leave against medical advice. if 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?

Answer 1

Explanation:

To calculate the probability that none of the selected subjects left the treatment center against medical advice, we need to know the total number of subjects transported by helicopter and the number of subjects who left against medical advice.

Let's assume the total number of subjects transported by helicopter is 'N' and the number of subjects who left against medical advice is 'A'.

The probability that none of the selected subjects left against medical advice can be calculated using the hypergeometric probability formula:

P(X = 0) = (C(A, 0) * C(N - A, n)) / C(N, n)

Where:

C(n, r) represents the number of combinations of selecting 'r' items from a set of 'n' items.

In this case, since we want to calculate the probability of selecting none of the subjects who left against medical advice, we set X = 0.

Substituting the values, we have:

P(X = 0) = (C(A, 0) * C(N - A, n)) / C(N, n)

Simplifying further:

P(X = 0) = (C(0, 0) * C(N - A, n)) / C(N, n)

Since C(0, 0) = 1 (by convention), the formula becomes:

P(X = 0) = (1 * C(N - A, n)) / C(N, n)

Now, you need to provide the values of 'N', 'A', and 'n' in order to calculate the probability.