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

Option D

D. $108

Step-by-step explanation:

We must calculate the expected cost per patient to use treatment method B.

The expected cost for a discrete random variable x is:

Where is the cost associated with the probability

In this case, the random variable x is represented by the cost of each treatment.

For treatment B there is a possibility that antibiotic 2 works, in that case the cost x would be $ 100 and

There is also the possibility that it does not work, in this case the cost x would be $180 and the probability

The expected cost  is:

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