In a regular physical check, Peter received a doctoral report, which stated that

ID: 3305092 • Letter: I

Question

In a regular physical check, Peter received a doctoral

report, which stated that “The test for lupus indicates that

you may have it. However, about 5% normal population

without lupus test positive. We will arrange more accurate

DNA-based test for you. Please contact our office for an

appointment.” Lupus is a chronic autoimmune disease

characterized by inflammation in one or more parts of the

body. Peter was very worried and found out that on

average 1 out of every 1000 Canadians suffer lupus (see

http://www.lupuscanada.org/). Suppose that the test used

by the doctor can identify 100% of the patients with lupus.

Based on the numbers given above, can you find the

chance that Peter does have lupus? Your calculation may

save him from many sleepless nights before he receives

the accurate DNA-based test result.

P(Lupus) = 1/1000 = 0.001

So,

P(Not Lupus) = 1 - 0.001 = 0.999

P(Positive| Lupus) = 1

P(Positive| Not Lupus) = 0.05

So,

P(Lupus| Positive)

= (0.001*1)/(0.001*1 + 0.999*0.05)

= 0.0196

So,

There is only 1.96% chance that Peter has it if the test says that he may have it.

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