Antibiotic resistance occurs when diseasecausing microbes be

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, 5% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 13 cases of gonorrhea during one week in 2004.

D) What is the probability that 1 or more out of the 13 were resistant to ciprofloxacin? (Hint: It is easier to first find the probability that exactly 0 of the 13 cases were resistant.)

Solution

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, 5% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 13 cases of gonorrhea during one week in 2004.

D) What is the probability that 1 or more out of the 13 were resistant to ciprofloxacin? (Hint: It is easier to first find the probability that exactly 0 of the 13 cases were resistant.)

Binomial distribution used.

p=0.05

n=13

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

P(X=x) = (_nC_x) p^x (1-p)^n-x

P(X=0) = (₁₃C₀) 0.05⁰ (1-0.05)^13-0

P( x=0)= 0.5133

P( x 1) = 1- P (x=0) = 1-0.5133 =0.4867

Answer: P=0.4867