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

Answer:

A

Explanation:

The probability that it would fail it's just 10% to a whole 90%

Answer 2

The expected cost per patient under plan B is gotten as; D: $108

How to solve random cost variable?

The expected cost for a discrete random variable x is given by the formula;

C = ∑xi * P(xi)

Where;

xi is the cost associated with the probability

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

For treatment B, there is a possibility that antibiotic 2 works, and in that case the cost x would be $ 100 and P(x) = 0.9

We are told that there is also the possibility that it does not work, and as such, the cost x would be $180 and the probability P(x) = 0.1

Thus, the expected cost is;

C = (100 * 0.9) + (180 * 0.1)

C = $108

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