10. Antibiotic resistance occurs when disease-causing microbes become resistant

Question

10. Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generation of microbes, it is a very serious public health problem. According to the CDC, 60% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 5 cases of gonorrhea during one week of 2004. Find the probability that at least 2 cases were resistant to ciprofloxacin. Round your answer to 4 decimal places.

Explanation / Answer

This is a case of binomial distribution

P(X) = nCx px qn-x

Here, n = 5

p = 0.6

q = 1 - p = 0.4

P(at least 2) = 1 - P(less than 2)

= 1 - P(0) - P(1)

= 1 - 0.45 - 5C1 x 0.6x0.44

= 0.9130

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