U represents drug user and NU represent Non-drug User. ++ result (test indicate drug user) and -- result (test indicate non-drug user)
U |
NU |
++ (0.99)
-- (0.01)
|
++ (0.02)
-- (0.98)
|
Given P(U) = 0.5/100 P(NU) = 1 - P(U) = 0.995
We want to find P(U / ++) = $\frac {P(U) * P(++ / U)} {P(++)}$
= $\frac {P(U) * P(++ / U)} {P(U) * P(++ / U) + P(NU) * P(++ /NU)}$
=$\frac {0.005 * 0.99} {0.005 * 0.99 + 0.995 * 0.02}$
= 0. 199