Question

10% of men without and 30% of men with test positive for a certain disease. What are the false positive and false negative rates of the test?

Answer 1

Out of all men... \(10\%+30\%=40\%\) test positive, be it false or true.

Answer 2

Thus \(100\%-40\%=60\%\) test negative, be it false or true.
We want to know which of these are false though.

Answer 3

I'm not sure if 10% would be the false positive rate. It states that 10% of men without the disease test positive for it, not that 10% of men who take the test are falsely diagnosed

Answer 4

Is this a probability class?

Answer 5

yes

Answer 6

Okay, let's say \(A\) is the event you have it. \(B\) is the even you test positive.

Answer 7

\[
\Pr(A^C|B)
\]This represents false positives, right?

Answer 8

yes, that makes sense to me

Answer 9

\[
\Pr(A^C|B)=\frac{\Pr(A^C\cap B)}{\Pr(B)}
\]

Answer 10

Now you claimed that \(10\%\) would be \(\Pr(A^C\cap B)\).

Answer 11

I believe that \[
\Pr(B) = \Pr(A^C\cap B)+\Pr(A\cap B)=0.10+0.30=0.40=40\%
\]

Answer 12

So \[
\Pr(A^C|B) = \frac{0.1}{0.4}=\frac 14=0.25 = 25\%
\]Does this make sense. Can you buy that?

Answer 13

Doesn't make a whole lot of sense somehow.

Answer 14

I think \(\Pr(A^C\cap B)=10\%\) is rate of false positives. Remember that \(10\%\) is of the total population, not only of those who are tests.

You tricked me man.

Answer 15

Yes, it's not 10% of the men tested. But it isn't 10% of the total population either, it is 10% of the population that doesn't have the disease.

Answer 16

So \(\Pr(B|A^C)=10\%\)?

Answer 17

Thats how I'm understanding the questions

Answer 18

\[
\Pr(B|A) = 30\%
\]

Answer 19

I almost feel like there isn't enough information. I think that if we knew the probability that a man would have the disease then it would be much easier