A company\'s management is worried about employee drug use and is instituting a

Question

A company's management is worried about employee drug use and is instituting a policy of mandatory drug tests. If an employee is a drug user, there is an 85% chance that he or she will test positive. If the employee is not a drug user, there is a 95% chance that he or she will test negative. Individuals who test positive are fired. We do not know the fraction of employees who are drug users. We do know, however, that 10% of all employees tested positive.

A) What fraction of employees are drug users?
B) Of those who test positive, what fraction are in fact not drug users?

Explanation / Answer

Let x be drug users, y be non drug users. So .85x +.05y= .10(x+y) .85x+.05y= .10x+.10y .75x= .05y x/y= .05/.75=5/75 So 5/5+75= 5/80= 0.0625 is the fraction of employees that are drug users. So 0.0625* .85 = 0.052125 are the drug users who test positive and .9375 *.05= 0.046875 are the non drug users who test positive. .046875/(.046875+.052125)= .46875 is the fraction of nondrug users who test positive.

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