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A test for a certain drug produces a false negative 4% of the time and a false positive 6% of the time. Supposed 19% of the employees at a certain company use the drug. If an employee at the company tests negative, what is the probability that he or she does not use the drug

Respuesta :

Answer:0.806

Step-by-step explanation:

Given

4 % Test false negative i.e. Person is drug user but test is negative

so 96 % are drug user and should with positive test

6 % is false Positive i.e. Person is Non-druggist but test is showing positive

94 % are Non-druggist and test negative

If 19 % of employees use drug

so 100-19=81 % are non drug user

Probability(Employee uses drug if he tests negative)=P

[tex]P=\frac{0.81\times 0.94}{0.81\times 0.94+0.19\times 0.04}[/tex]

[tex]P=\frac{0.761}{0.943}=0.806[/tex]

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