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4 votes
4 votes

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

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