Question

a study of helicopter usage and patient survival, among the 56,142 patients transported by helicopter, 297 of them left the treatment center against medical advice, and the other 55,845 did not leave against medical adviceIf 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

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)

Explanation:

To find the probability that none of the 40 subjects randomly selected left the treatment center against medical advice, we can use the formula for combinations. The number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice is given by C(55,845, 40), which can be calculated as:

C(55,845, 40) = 55,845 choose 40 = (55,845!) / (40! * (55,845 - 40)!)

The probability that none of the 40 subjects randomly selected left the treatment center against medical advice is given by the number of ways to choose 40 subjects out of 55,845 that did not leave against medical advice, divided by the number of ways to choose 40 subjects out of 56,142 total subjects:

P = C(55,845, 40) / C(56,142, 40) = (55,845!) / (40! * (55,845 - 40)!) / (56,142!) / (40! * (56,142 - 40)!)