Question

A sports club tests its players for steroid usage with a test that gives a positive reading 93% of the time when administered to a steroid user and gives a negative reading 96% of the time when administered to a player who does not use steroids. It is known that 8% of the players are steroid users. Draw a probability tree diagram for the given problem.
What is the probability that a player does not use steroids, given that the person had a positive reading on the test? Round your answer to four decimal places.

Answer 1

Answer:

P(no steroid user / positive reading on test) = 0.3309

Step-by-step explanation:

Computation:

Bayes' Theorem:

P(A / B) = P(A and B) / P(B)

P(no steroid user / positive reading on test) = P(no steroid user and positive) / P(positive)

P(no steroid user / positive reading on test) =  (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)

P(no steroid user / positive reading on test) = 0.3309