MathProblem 34 Drug test problem
10% of the people in a certain population use an illegal drug. A drug test yields the correct result 90% of the time, whether the person uses drugs or not. A random person is forced to take the drug test and the result is positive. What is the probability he uses drugs?
Solution
利用全概率公式：
\[P(use|positive) = \frac{P(positive|use)\cdot P(use)}{P(positive|use)\cdot P(use)+P(positive|unuse)\cdot P(unuse)}\\
=\frac{0.9\times 0.1}{0.9\times 0.1+0.1\times 0.9}=\frac{1}{2}
\]
