Antibiotic resistance occurs when disease-causing microbes become resistant to a

Question

Antibiotic resistance occurs when disease-causing microbes become resistant to antibiotic drug therapy. Because this resistance is typically genetic and transferred to the next generations of microbes, it is a very serious public health problem. According to the Centers for Disease Control and Prevention (CDC), 27% of gonorrhea cases tested in 2010 were resistant to at least one of the three major antibiotics commonly used to treat gonorrhea. A physician treated 9 cases of gonorrhea during one week of 2010.

(a) What is the probability (±0.0001) that exactly 2 out of the 9 cases was resistant to at least one of the three major antibiotics?

(b) Find the probability (±0.0001) that 1 or more out of the 9 were resistant to at least one of the three major antibiotics.

(Hint : It is easier to first find the probability that exactly 0 of the 9 cases were resistant.)

Explanation / Answer

PROBABILITY THAT THE RESISTANT TO AT LEAST ONE OF THE MAJOR ANTIBIOTICS = 0.27

A) TOTAL CASES TESTED = 9

P(X=2, 2 CASES ARE RESISTANT) = 9C2*(0.27)^2*(0.73)^7 = 0.2899

B) P( AT LEAST 1 IS RESISTANT) = 1 - P(0 RESISTANT)

P(0) = 9C0*(0.27)^0*(0.73)^9 = 0.0588

THEREFORE P(AT LEAST 1) = 1 - 0.0588 = 0.9412

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