Question

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 probability that a patient treated under plan A will be successfully treated?
A. 0.98
B. 0.72
C. 0.80
D. 0.90

Answer 1

Answer: Option A

A. 0.98

Step-by-step explanation:

Plan A consists of:

Plan A: treat with antibiotics 1. If not effective, treat with antibiotics 2

Antibiotic 1 has a probability P (1) of 0.8 to be effective

Antibiotic 2 has a probability P (2) of 0.9 to be effective.

For a patient to be treated successfully with plan A it can happen that:

The antibiotic 1 works, or that the antibiotic 1 does not work but the 2 antibiotic if it works.

So the probability that plan A works is:

$P = P (1) + P (not\ 1) P (2)\\\\P = 0.8 + (1-0.8) (0.9)\\\\P = 0.8 + 0.2 * 0.9\\\\P = 0.98$