Mathematics, 13.03.2020 03:10, cris6969

All athletes at the Olympic Games (OG) are tested for performance-enhancing steroid drug use. The basic Anabolic Steroid Test (AST) test gives positive results (indicating drug use) for 90% of all steroid-users but also (and incorrectly) for 2% of those who do not use steroids. Suppose that 5% of all registered athletes use steroids. Based on this information compute the following probabilities.

(a) What is the probability that an athlete uses steroids and the AST test fails to detect it?
(b) What is the probability that a randomly selected athlete will get a positive AST?
(c) If an athlete has tested negative, what is the probability that he/she does not use steroids?
(d) Is "testing positive" statistically independent of "using steroids"? Clearly prove your answer.
(e) [Bonus 1pts] What is the probability that the athlete will either use steroids or she/he will get a positive result?

Answers: 2

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All athletes at the Olympic Games (OG) are tested for performance-enhancing steroid drug use. The ba...