Question

Select the correct answer.
Two different antibiotics can be used to treat an infection. Treatment with antibiotic 1 is known to be successful 80% of the time. This treatment costs $80. Antibiotic 2 is successful 90% of the time and costs $100.

The two treatment plans are:

Plan A: Treat with antibiotic 1. If not effective, treat with antibiotic 2.
Plan B: Treat with antibiotic 2. If not effective, treat with antibiotic 1.
Based on the data provided, what is the expected cost per patient under plan B?

A.
$100

B.
$80

C.
$180

D.
$108

Answer 1

Plan B always uses antibiotic 2 ($100). With probability 0.1 it fails and you then use antibiotic 1 ($80).
Expected cost = $100 + 0.1($80) = $100 + $8 = $108.

Answer: D.