MathProblem 34 Drug test problem

标签：0.9 use 0.1 positive MathProblem times 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：

\[P(use|positive) = \frac{P(positive|use)\cdot P(use)}{P(positive|use)\cdot P(use)+P(positive|unuse)\cdot P(unuse)}\\ =\frac{0.9\times 0.1}{0.9\times 0.1+0.1\times 0.9}=\frac{1}{2} \]

标签：0.9,use,0.1,positive,MathProblem,times,test,problem
From： https://www.cnblogs.com/xinyu04/p/16586927.html