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All athletes at the Olympic games are tested for performance-enhancing steroid drug use. The imperfect test gives positive results (indicating drug use) for 92%

All athletes at the Olympic games are tested for performance-enhancing steroid drug use. The imperfect test gives positive results (indicating drug use) for 92% of all steroid-users but also (and incorrectly) for 5% of those who do not use steroids. Suppose that 8% of all registered athletes use steroids. If a random athlete has tested negative, what is the probability that they use steroids? Give the answer below as a percentage rounded to two decimal places (but don't use the % sign). All (8 points) supporting work must be submitted on your scratch paper.

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