A rare virus that produces flu like symptoms in its victims is present in a metr

Question

A rare virus that produces flu like symptoms in its victims is present in a metropolitan community. The probability a random person is infected with it is 0.0085 or eighty-five persons in 10,000. There is a test to check whether or not a person has been infected with the virus. The test is 92% accurate but suffers from a 4% false positive rate. If public health officials in the community perform random testing and a person test positive, what is the true probability they are infected with the virus?

Explanation / Answer

Ans:

Given that

P(infecttion)=0.0085

P(positive/infection)=0.92

P(positive/no infection)=0.04

P(positive)=P(positive/infection)*P(infection)+P(positive/no infection)*P(no infection)

=0.92*0.0085+0.04*(1-0.0085)=0.04748

We have to find:

P(infection/positive)=P(positive/infection)*P(infection)/P(positive)

=0.92*0.0085/0.04748=0.1647

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.