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A sports club tests its players for steroid usage with a test that gives a positive...

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 to use steroids. It is known that 8% of the players are steroid users.

a. Draw a probability tree diagram for the given problem showing all probabilities. b. What is the probability that a player does not use steroids given, that the person had a positive reading on the test? Show the formula you use and all calculations.

math   Statistics-And-Probability   
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Answer #1

a) Tree Diagram

b) Bayes' Theorem: P(A | B) = P(A & B) / P(B)

P(not a steroid user | positive reading on the test) = P(not a steroid user and positive) / P(positive)

= (0.92 x 0.04)/(0.08 x 0.93 + 0.92 x 0.04)

= 0.3309

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