Answer:
probability that an athlete who tests positive is actually a user
= 0.2177
Step-by-step explanation:
To solve this problem, we create a table that relates the test results and the status of the athletes.
We arbitrarily take a sample of 10000 atheletes to work with whole numbers.
Out of that, 300 are users (3% on the average), and 9700 are non users.
Of the users, 270 users will test positive (90% accuracy) and 30 will test negative.
Similarly, of the non-users, 970 will test positive, and 8730 will test negative.
This gives 1240 positive tests, and 8760 negative tests.
Of the 1240 who test positive, 270 are actually users.
Therefore the probability of the positive test results are actually users
= 270/1240 = 0.2177
