Test Study New Drug Probability

Question

In a study, a new drug is found to be effective in 67% of those who took it. 14% of people in the study overall reported mild side effects (soreness, headache or nausea). Also, of the people for whom the drug was effective, 18% reported minor side effects.

Part a)

Based on this study, what is the probability that a sick person who takes the drug will both quickly recover (that is, the drug is effective) and experience minor side effects? Do NOT round answer

Part b)

Suppose a sick person takes the drug. If they experience a side effect, what is the probability the drug will be effective? Do NOT round answer.

Answer 1

100 patients take a new drug and 67 report good effects.

14 of the 100 patients say they had mild discomfort.

Of the 67 patients with favorable results, 18% (or 12.06 patients)

said they had mild discomfort along with the good effects.

P(Good Effects And Mild Discomfort) is given by 0.67 times 0.14 or 0.0938.

P(Good Effects Given Mild Discomfort) is given by:

---------------------------[P(Good Effects) Times P(Mild Discomfort Given Good Effects)]-------------------------

------------------------------------------------------------Divided By-------------------------------------------------------------

[P(Good Effects) Times P(Mild Discomfort Given Good Effects) Plus P(Other Effects) Times P(Mild Discomfort Given Other Effects)].

Placement of values gives [(0.67) × (0.18)] Divided By [(0.67) × (0.18) + (0.33) × (14 − 12.06)/33] which

simplifies to 0.8614285714.