Question

Problem 6

Two antibiotics A and B are available as a treatment for a common ear infection in children.

Antibiotic A is known to cure the infection 86 % of the time. Treatment with Antibiotic A costs

$ 70. Antibiotic B is known to cure the infection 91 % of the time. Treatment with Antibiotic B

costs $ 85. The antibiotics work independently of one another. A health insurance company

intends to recommend one of the following two plans of treatment for children with this ear

infection.

Plan 1 : Treat with antibiotic A first. If it’s not effective, then treat with antibiotic B.

Plan 2: Treat with antibiotic B first. If it’s not effective, then treat with antibiotic A.

a) (i) If a doctor treats a child using plan 1, what’s the probability that the child will be cured ?

(ii) If a doctor treats a child using plan 2, what’s the probability that the child will be cured?

b) (i) Compute the expected cost per child when plan 1 is used for treatment.

(ii) Compute the expected cost per child when plan 2 is used for treatment.

c) Based on the results above, which plan would you recommend? Justify your answer

Answer 1