Question

Two antibiotics are available as treatment for an ear infection in children. Antibiotic A cures the infection 60% of the time, and Antibiotic B cures 90% of the time. The antibiotics work independently of one another. A doctor will recommend one of the two plans.

o Plan I: Treat with antibiotic A first. If it does not cure the infection, treat with antibiotic B.

o Plan II: Treat with antibiotic B first. If it does not cure the infection, treat with antibiotic A

(1) (4pts) If a doctor treats a child using Plan I, what is the probability that the child will be cured?

(2) (3pts) If a doctor treats a child using Plan II, there is a 96% chance that the child will be cured. The expected cost for Plan I is $83 and the expected cost for Plan II is $79. Using these results and the result from (1), which plan (Plan I or Plan II) would you recommend? Explain why.

Answer 1

1) Probability that with plan I, the child will be cured is computed here as:

= Probability that the child will be cured with antibiotic A + Probability that the child will not be cured with antibiotic A * Probability that the child will be cured with antibiotic B

= 0.6 + (1 - 0.6)*0.9 = 0.96

Therefore 0.96 is the required probability that the child will be cured here.

2) Given that both have an equal chance of curing the child that is 96% in both the cases, and the cost for plan I is $4 more than the cost for plan II, therefore we would recommend plan II here.