In a commissioned research, the inter-collegiate swim meets management found out that an estimated that 3% of the swimmers competing are users of performance-enhancing drugs. When athletes test for use of these types of drugs, the result is 90% accurate. What is the probability that a swimmer who tests positive for the performance-enhancing drug is actually a user?
In a commissioned research, the inter-collegiate swim meets management found out that an estimated that 3% of the swimmers competing are users of performance-enhancing drugs. When athletes test for use of these types of drugs, the result is 90% accurate. What is the
Given
The percentage of swimmers competing use performance enhancing drugs = 3%
The accuracy of the test = 90%
The probability that test show correct result = 0.90
The probability that test show incorrect result = 0.10
The probability that swimmer use drug = 0.03
The probability that swimmer do not use drug = 0.97
The probability that swimmer use drug and show positive = 0.03*0.90 = 0.027
The probability that swimmer do not use drug and show positive = 0.97*0.10 = 0.097
The total probability of testing positive = 0.027+ 0.097 = 0.124
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