Antibiotic for blood infections.Enterococci are bacteria that cause blood infections in hospitalized patients. One antibiotic used to battle enterococci is vancomycin. A study by a large nationwide health system revealed that 8% of all enterococci in its hospitals were resistant to vancomycin. Consider a random sample of four patients with blood infections caused by the enterococci bacterium. Suppose that all four patients are treated with the antibiotic vancomycin.

Note: Give your answers in decimal form with at least four decimal places.

a) What is the probability that all four patients are treated successfully?

b) What is the probability that the bacteria resist the antibiotic in at least one patient?