Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given
That the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the
Athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a
Positive test result has been observed for an athlete, what is the probability that they have taken
This steroid?
A)0.9928
B)0.9552
C)0.0995
D)0.9325

Question

Quizplus · Accepted Answer

To find the probability that an athlete has taken the steroid given a positive test result, we use Bayes' theorem. Let A be the event that the athlete has taken the steroid, and B be the event of a positive test result. We need to find P(A|B).P(A|B) = [P(B|A) * P(A)] / [P(B|A) * P(A) + P(B|A') * P(A')]Given:- P(A) = 0.10 (probability of taking the steroid)- P(A') = 0.90 (probability of not taking the steroid)- P(B|A) = 0.995 (probability of a positive test if the steroid is taken)- P(B|A') = 1 - 0.992 = 0.008 (probability of a positive test if the steroid is not taken)Plugging in the values:P(A|B) = [0.995 * 0.10] / [(0.995 * 0.10) + (0.008 * 0.90)]       = 0.0995 / (0.0995 + 0.0072)       = 0.0995 / 0.1067       ≈ 0.9325Therefore, the probability that an athlete has taken the steroid given a positive test result is approximately 0.9325.

Suppose the Probability of an Athlete Taking a Certain Illegal