Olympics: Steroid Testing. Use of performance enhancing drugs in the Olympics have always been frowned upon and has led to many participants being either disqualified or banned from participating in athletic competitions. Suppose that a steroid test was conducted prior to the 2020 Olympics to determine whether a participant is able to participate. Historically, the percentage of athletes known to use steroids was 1%. Furthermore, those participants who ended up testing positive during the first round of testing were 3%. However, clinical research shows that the steroid test being used is known to be 99% effective (that is,

99% of steroid users will test positive) with a false positive rate of 2% (that is, 2% of the time those athletes who test positive are not steroid users). Let A be the event that an athlete is a steroid user and B be the event that the athlete is not a steroid user. Let C be the event that the athlete tests positive for steroids and D be the event that the athlete tests negative for steroids. Compute the following:

(a) P(A), P(B), P(C), P(D)

(b) P(A and C) and P(B and D)

(c) P(A or C)

(d) P(A | C) and P(C | A)

(e) Interpretation What is the contextual difference between the two conditional probabilities found in (d)? Hint: If you were an athlete who suddenly tested positive during testing, which probability would impact you more?
Brain Teasers Assume A and B are events such that 0 , P(A) , 1 and 0 , P(B) , 1. Answer questions 42–56 true or false and give a brief explanation for each answer. Hint: Review the summary of basic probability rules.

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