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
