Question

In a study of helicopter usage and patient​ survival, among the 44,220 patients transported by​ helicopter, 175 of them left the treatment center against medical​ advice, and the other 44,045 did not leave against medical advice. 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?

The probability is .

Answer 1

To find the probability that none of the 50 selected subjects left the treatment center against medical advice, we need to calculate the probability of each subject not leaving against medical advice and multiply these probabilities together. The probability is 0.7794, or 77.94%.

Step-by-step explanation:

To find the probability that none of the 50 selected subjects left the treatment center against medical advice, we need to calculate the probability of each subject not leaving against medical advice and then multiply these probabilities together.

The probability that the first subject did not leave against medical advice is given by:

P(Not leaving) = (44,045/44,220) = 0.9958

Since we are selecting without replacement, the probability that the second subject did not leave against medical advice is given by:

P(Not leaving) = (44,044/44,219) = 0.9958

Continuing this process for all 50 subjects, we multiply the probabilities together:

P(None left against medical advice) = (0.9958)(0.9957)...(0.9892) = 0.7794

Therefore, the probability that none of the 50 selected subjects left the treatment center against medical advice is 0.7794, or 77.94%.