Question

n a study of helicopter usage and patient survival, among the 56,896 patients transported by helicopter, 168 of them left the treatment center against medical advice, and the other 56,728 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?

Answer 1

The probability that none of the 40 subjects selected left the treatment center against medical advice is approximately 0.875164.

Step-by-step explanation:

To find the probability that none of the 40 subjects selected left the treatment center against medical advice, we need to find the probability that each subject did not leave against medical advice.

The proportion of subjects who did not leave against medical advice in the population is:

p = (56,728 - 168) / 56,896 ≈ 0.997067

The probability that each subject in the sample did not leave against medical advice is approximately equal to the population proportion. Therefore, the probability that none of the 40 subjects left against medical advice is:

P(X = 40) = p^40 ≈ 0.997067^40 ≈ 0.875164