A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time.Further, 15% of all steroid-free individuals also test positive.10% of the rugby team members use steroids.Your friend on the rugby team has just tested positive.The probability that he uses steroids is ________________________ .
A)0.4130
B)0.8636
C)0.0950
D)0.2300

Question

Quizplus · Accepted Answer

To solve this, we use Bayes' theorem. Let A be the event that a person uses steroids, and B be the event that a person tests positive. We're given P(B|A) = 0.95 (probability of testing positive given steroid use), P(A) = 0.10 (probability of being a steroid user), and P(B|A') = 0.15 (probability of testing positive without using steroids, where A' is the complement of A). We want to find P(A|B), the probability that a person uses steroids given that they tested positive.P(A|B) = [P(B|A) * P(A)] / [P(B|A) * P(A) + P(B|A') * P(A')]P(A') = 1 - P(A) = 0.90 (probability of not being a steroid user).P(B) = P(B|A) * P(A) + P(B|A') * P(A') = 0.95 * 0.10 + 0.15 * 0.90 = 0.095 + 0.135 = 0.230.So, P(A|B) = (0.95 * 0.10) / 0.230 = 0.095 / 0.230 = 0.4130.Therefore, the probability that your friend uses steroids, given that he has tested positive, is 0.4130.

A Manufacturer Claims That Its Drug Test Will Detect Steroid