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8 percent of all adults over 50 have diabetes; a health clinic diagnoses 95 percent of all people with diabetes correctly and 2 percent incorrectly.

(a) Probability that it will diagnose someone above 50 with diabetes

(b) correctly diagnose that person

I think I'm close, but need help

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If you think you are close, please show what you have done. It allows much more helpful answers. –  Ross Millikan Feb 11 '13 at 19:28
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Since $95+2\ne 100$, are we to assume that in $3$ percent of the cases the test is inconclusive? And what does the test do with people who do not have diabetes? Has the original problem been fully written out above? –  André Nicolas Feb 11 '13 at 19:36
    
I was thinking for part (a) that these are independent events and that I should multiply the probability of having diabetes above 50 (.08) by .94 and add this with (.08)(.02) because in the second part is actually asking for being correctly diagnosed. Is this correct? –  JuanSancen Feb 11 '13 at 19:57
    
The problem indicates that 95 percent of the time it accuartely diagnoses people with diabetes and 2 percent inacurately. –  JuanSancen Feb 11 '13 at 20:01
    
I meant to say .95 –  JuanSancen Feb 11 '13 at 20:01

1 Answer 1

Hint

Assume that there are 10,000 adults over fifty and they all go to the health clinic.

How many (the actual number) of the 10,000 have diabetes? How many (again: the actual number) of that group will be diagnosed-with-diabetes?

How many of the 10,000 do not have diabetes? How many of that group will be diagnosed-with-diabetes?

How many of the 10,000 will therefore be diagnosed-with-diabetes? How many of that group indeed have diabetes?

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