Antibiotic resistance. Antibiotic resistance occurs when disease-causing microbe

Question

Antibiotic resistance. 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 CDC, approximately 30% of gonorrhea cases tested in 2011 were resistant to at least one of the three major antibiotics commonly used to treat gonorrhea. A physician treated 10 cases of gonorrhea during one week of 2011.

(a) What is the distribution of the cases resistant to at least one of the three major antibiotics? Not binomial or Binomial?

(b) What is the probability that exactly one out of the 10 cases was resistant to at least one of the three major antibiotics? (Round your answer to four decimal places.) P(X=1)= What is the probability that exactly two out of the 10 cases was resistant to at least one of the three major antibiotics? (Round your answer to four decimal places.) P(X=2)= ?

(c) Also find the probability that one or more out of the 10 were resistant to at least one of the three major antibiotics. (Hint: It is easier to first find the probability that exactly zero of the 10 cases were resistant.) (Round your answer to four decimal places.) P(X1)=?

Explanation / Answer

(a)Yes, the distribution of the cases resistant to at least one of the three major antibiotics is binomial. The two outcomes here is either resistant or not. That is success and failure.

(b)Let X= the cases resistant to at least one of the three major antibiotics

X follows Binomial (10,0.30)

Find P(X=2)

=10C2*0.30^2*0.70^8

=0.233

(c)Find P(X>=1)

=P(X=0)

=10C0*0.30^0*0.70^10

=0.028

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.