USA Today reported (“Study Finds Better Survival Rates at ‘High-Volume’ Hospitals”) that “high-volume” hospitals performed at least 77% of bladder removal surgeries; “low-volume” hospitals performed at most 23%. Assume the percentages are 77% and 23%. In the first two weeks after surgery, 3.1% of patients at low-volume centers died, compared to 0.7% at the high-volume hospitals.
a. Calculate the probability that a randomly chosen bladder-cancer patient had surgery at a high-volume hospital and survived the first two weeks after surgery.
b. Calculate the probability that a randomly chosen bladder-cancer patient survived the first two weeks after surgery.
c. If two bladder-cancer patients were chosen randomly, determine the probability that only one would survive the first two weeks after surgery.
d. If two bladder-cancer patients were chosen randomly, determine the probability that at least one would survive the first two weeks after surgery.