MATH SOLVE

7 months ago

Q:
# 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?\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.

Accepted Solution

A:

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.)

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.)