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 the federal Centers for Disease Control and Prevention revealed that 8% of all enterococci isolated in hospitals nationwide were resistant to vancomycin. (New York Times, Sept. 12,1995.) Consider a random sample of three patients with blood infections caused by the enterococci bacterium. Assume that all three patients are treated with the antibiotic vancomycin.
a. What is the probability that all three patients are treated successfully? What assumption did you make concerning the patients?
b. What is the probability that the bacteria resist the antibiotic in at least one patient?
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