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 generation of microbes, it is a very serious public health problem. According to the CDC, 6% of gonorrhea cases tested in 2004 were resistant to the antibiotic ciprofloxacin. A physician prescribed ciprofloxacin for the treatment of 18 cases of gonorrhea during one week in 2004

a. binomial, n=18 p=0.06

b.probability of exactly 1 of the 18 cases were resistant 0.377

need help with c and d

(c) What is that probability for exactly 2 out of 18?

(d) What is the probability that 1 or more out of the 18 were resistant to ciprofloxacin? (Hint: It is easier to first find the probability that exactly 0 of the 18 cases were resistant.) mean is 1.08 standard deviation is 1.008

Please show the work, I want to understand how to solve for other questions. thanks in advance!

Answer 1

P(X = x) = nCx * p^x * (1 - p)^{n - x}

c) P(X = 2) = 18C2 * (0.06)^2 * (0.94)^16 = 0.2047

d) P(X > 1) = 1 - P(X < 1)

                   = 1 - P(X = 0)

                   = 1 - 0.3283

                   = 0.6717