5. A medical test classifies subject as being either positive (infected with vir

Question

5. A medical test classifies subject as being either positive (infected with virus) or negative (not infected). The test is believed to be 99% accurate. In other words, if an infected person is tested, it is 99% likely that his/her result is positive; while if a healthy (non- infected) person is tested, it is 99% likely that his/her result is negative. Suppose that 5% of all people are infected and 95% are healthy. If a randomly selected person is tested to be positive, what is the probability that person is actually infected? (10)

Explanation / Answer

5)probabilty test is poisitve =P(P)

probabilty of healthy people =P(H) =0.95

probability of infected people =P(I) =0.05

as test is accurate 99% of times

hence probabilty of +ve given person is healthy =P(P|H) =0.01

and probabilty of +ve given person is healthy=P(P|I)=0.99

hence probabilty that test is positive =P(P)=P(H)*P(P|H)+P(I)*P(P|I) =0.01*0.95+0.99*0.05=0.059

therefore probabilty of a person to be infected given test is positive =P(I|P) =P(I)*P(P|I)/P(P) =0.99*0.05/0.059

=0.839

6)probabilty that system works =P(component 1 works*component 2 works*component 3 works)

=(1-0.05)*(1-0.15)*(1-0.1)=0.72675

7)a) discrete

b)discrete

c)discrete

d)continuous

e)continuous

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

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