In a study of helicopter usage and patient survival, results were obtained from 47,637 patients transported by helicopter and 111,874 patients transported by ground (based on data from "Association Between Helicopter vs Ground Emergency Medical Services and Survival for Adults with Major Trauma," by Galvagno et al., Journal of the American Medical Association, Vol. 307, No. 15).
a. If 1 of the 159,511 patients in the study is randomly selected, what is the probability that the subject was transported by helicopter?
b. If 5 of the subjects in the study are randomly selected without replacement, what is the probability that all of them were transported by helicopter?
Find the probabilities and indicate when the "5% guideline for cumbersome calculations" is used.