Question

12. Suppose 500 athletes are tested for a drug, one in twenty has used the drug, the test has a 98% specificity and the test has a 100% sensitivity. That is, the probability of a false positive is 2% and there is no chance that the user of the drug will go undetected. Construct a tree diagram showing the probabilities associated with this problem. Write a probability on each branch (6 branches). Multiply the the probabilities along each path and write that number at the end of the path (4 answers).

13. Suppose one of the athletes in Question 12 tests positive. What is the probability that he or she has used the drug? (Express your answer as a decimal rounded to two decimal places.)

Answer 1

12)

let D+ is event of having taken drug and T+ is tested positive,

P(D+nT+)0.05 0.0500 P(T+ID+)=1 P{T-|D+)=0 P(D-J=0.05 P(D+nT.)=0 0.0000 P[D-NT+)=0.019 0.0190 PID-)-0.95 P(T+ID-)=0.02 P(T-10-)=0.98 P(D-NT-)=0.931 0.9310

13)

P(use the drug |test positive) =P(D+ |T+) =P(D+ and T+)/P(T+)=0.05/(0.05+0.019)=0.72