Question

. It is estimated that 3% of the athletes competing in a large tournament are users of an illegal drug to enhance performance. The test for this drug is 90% accurate. What is the probability that an athlete who tests positive is actually a user?

Answer 1

Answer:

the probability is 0.2177 (21.77%)

Step-by-step explanation:

defining the event T= the test is positive , then the probability of T is

P(T)= probability to choose an user of illegal drug * probability that the test be positive given that a user of illegal dug was selected + probability to not choose an user of illegal drug * probability that the test be positive given that a user of illegal dug was not selected = 0.03* 0.90 + 0.97*0.10 = 0.124

then we can use the theorem of Bayes for conditional probability , defining the event U= choosing an athlete that is a user , then

P(U/T)= P(U∩T)/P(T) =  0.03* 0.90/0.124 = 0.2177 (21.77%)

where

P(U/T)= probability that an athlete that is an user was chosen , given that the test was positive

P(U∩T)= probability of choosing an athlete that is an user and the test results positive