A new drug must succeed in four successive phases before it can be approved for public use
MATHEMATICS · Multi-part · AP · AP Statistics · Probability Random Variables Distributions · Probability Random Variables Distributions
Problem
A new drug must succeed in four successive phases before it can be approved for public use. Let S1,S2,S3, and S4 denote the events that the drug succeeds in the Pre-clinical study, Phase I trial, Phase II trial and Phase III trial respectively. The following probabilities are estimated:
P(S1)=0.80;
P(S2∣S1)=0.60;
P(S3∣S1∩S2)=0.50;
P(S4∣S1∩S2∩S3)=0.65.
If the drug fails at any phase, testing stops immediately and the drug is not approved.
(i) Find the probability that the drug is approved for public use (that is, it succeeds in all four phases).
(ii) Given that the drug is not approved, determine the probability that it failed specifically in Phase II.