Question

ts) A test for steroids has a 2% false positive rate and a 5% false negative rate. This means that 2% of ball players who do not take steroids test positive for them, and 5% of the steroid users test negative. Suppose that 1% of players use steroids: (a) What is the probability that someone who tests positive actually uses steroids? (b) What is the probability that someone who tests negative does not use stero

Answer 1

Answer and Step-by-step explanation:

             ------------ 1% uses steroids -------------- 95% tests + (OK!)

                                                       --------------   5% tests - (false negative)

Players

            -----------99% do not use steroids -------------- 98% tests - (OK!)

                                                                   -------------    2% tests + (false positive)

(a) What is the probability that someone who tests positive actually uses steroids?

In other words, whats the probability of a player using steroids given that the test is positive?

P(uses | test +) = P(uses ∩ test +)/P(test +)

P(uses ∩ test +) = 0.01*0.95 = 0.0095

P(test +) = 0.01*0.95 + 0.99*0.02 = 0.0293

P(uses ∩ test +)/P(test +) = 0.0095/0.0293 = 0.3242

(b) What is the probability that someone who tests negative does not use steroids?

In other words, whats the probability of a player not using steroids given that the test is negative?

P(not uses | test -) = P(not uses ∩ test -)/P(test -)

P(not uses ∩ test -) = 0.99*0.98 = 0.9702

P(test -) = 0.01*0.05 + 0.99*0.98 = 0.9707

P(not uses | test -) = P(not uses ∩ test -)/P(test -) = 0.9702/0.9707 = 0.9995