Question

Suppose two drugs are routinely used for treatment of a particular kidney disorder. Drug 1 is known to cure the disease 85% of the time and costs $90. Drug 2 is known to cure the disease 70% of the time and costs $65. The two drugs work independent of each other (that is, administration of one has no effect on the efficacy of the other). The two treatment plans are as follows:
Plan A: Treatment with Drug 1—if not effective, treatment with Drug 2.
Plan B: Treatment with Drug 2—if not effective, treatment with Drug 1.

Which statement is most correct in this situation?
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Based on the overall probability of a cure, plan A should be selected over plan B.
Based on the overall probability of a cure, plan B should be selected over plan A.
Based on the overall cost of treatment, plan A should be selected over plan B.
Based on the overall cost of treatment, plan B should be selected over plan A.
Based on the probability of a cure and the cost of treatment, both plans are equivalent, so either can be selected.

Answer 1

If we use Plan A, to start with drug 1, we spend $90. Then in the event that drug 1 did not work (1 - 85% = 15% chance), we spend $65 more for drug 2. This is an expected value of $90 + (0.15)($65) = $99.75.

If we use Plan B, to start with drug 2, we spend $65. And if it does not work (1 - 70% = 30% chance), we spend $90 more for drug 2. This is an expected cost of $65 + (0.3)($90) = $92

Therefore, based on the overall cost of treatment, plan B should be selected over plan A. (The probabilities will actually be the same after both drugs have been tried, in either order.)