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?

Answer 1

a.Based on the overall probability of a cure, Plan A should be selected over Plan B.
b.Based on the overall probability of a cure, Plan B should be selected over Plan A.
c.Based on the overall cost of treatment, Plan A should be selected over Plan B.
d.Based on the overall cost of treatment, Plan B should be selected over Plan A.
e.Based on the probability of a cure and the cost of treatment, both plans are equivalent, so either can be selected.

Answer 2

The overall probability of a cure with plan A is given by:
\[\large P(cure\ with\ plan\ A)=0.85+0.15\times0.7=0.955\]
The overall probability of a cure with plan B is given by:
\[\large P(cure\ with\ plan\ B)=0.7+0.3\times0.85=0.955\]
Therefore both plans have the same probability of a cure.
Let the cost of a cure be given by the variable X.
With plan A:
\[\large E(X)=90\times0.85+(90+65)\times(0.15\times0.7)=$92.78\]
With plan B:
\[\large E(X)=65\times0.7+(90+65)\times(0.3\times0.85)=$85.03\]
Can you now make the correct choice of answer?

Answer 3

D?

Answer 4

Yes, D is correct.