Q:

Suppose two drugs are routinely used for the treatment of thyroid dysfunction. Drug X is known to cure the disorder 75% of the time and costs $88. Drug Y is known to cure the disorder 60% of the time and costs $75. The two drugs work independent of each other. The two treatment plans are as follows:Plan A: Treatment with Drug X—if not effective, treatment with Drug YPlan B: Treatment with Drug Y—if not effective, treatment with Drug XFor what part of the population is Plan B NOT effective?40%30%15%10%

Accepted Solution

A:
Answer: the last option: 10%

Explanation:

1) Plan B: Treatment with Drug Y—if not effective, treatment with Drug X

2) The two drugs work independent of each other => joint probability equals the product of the individual probabilities.

3) probability of drug y is not effective = 1 - probability of being effective = 1 - 0.6 = 0.4

4) probability of drug x is not effective = 1 - probability of being effective = 1 - 0.75 = 0.25

5) Joint probability of being not effective = 0.4 × 0.25 = 0.10

6) 0.10 = 10%

Therefore the answer is 10%