Question

1. A pharmaceutical trial tests the effectiveness of 3 different drugs (A, B, and C) for relieving arthritis symptoms. 30% of the participants in the trial are given drug A. Of those, 70% experience relief from their symptoms (event R). 32% of participants are given drug B, of which 80% experience relief. The remaining 38% of participants are given drug C, of these 53% experience relief.

a. What’s the probability that a participant did not experience relief if they took drug B?

b. What’s the probability that a participant experienced relief given that they did not take drug C?

c. What is the probability that a participant in the trial gets relief from their symptoms?

d. If a participant experience relief, what is the probability that they took drug C?

e. If a participant did not experience relief from their symptoms, what is the probability that they took drug A?

Answer 1

a)

P(not experience relief |B) = P(Rc|B) =1-P(R|B )=1-0.80 =0.2

b)

P(R|not C) =P(R |A or B) =(P(A n R)+P(B n R)/(P(A)+P(B)) =(0.3*0.7+0.32*0.8)/(0.3+0.32)=0.7516

c)

P(R) =P(A)*P(R|A)+P(B)*P(R|B)+P(C)*P(R|C)=0.3*0.7+0.32*0.8+0.38*0.53 =0.6674

d)

P(C|R )=P(C)*P(R|C)/P(R) =0.38*0.53/0.6674 =0.3018

e)

P(A|Rc) =P(A)*P(Rc|A) /P(Rc) =0.3*(1-0.7)/(1-0.6674)=0.2706