Using Bayes' Theorem to find probability of disease | screen negative

Question

I have a problem to solve and i can't figure out how. I have the following data:

P(screen positive| disease) = 0.7
P(screen negative| no disease) = 0.9
P(Disease) = 0.01

The answer for this problem according to my teacher is 0.04 but i can't reach it.

The formula i tried to use is and the result i got with it is 0.03 :

Is my teacher wrong or am i not using the correct formula, in which case, what is the solution ?

Answer 1

I think you are right.

If you take $1000$ "typical" people, based on the given data:

$990$ people do not have the disease. Of these, $891$ will screen negative.

$10$ people do have the disease. Of these, $3$ will screen negative.

Altogether, there will be $894$ negative screens, of which $3$ have the disease.

So $P($ disease $\mid$ negative screen $)=\frac{3}{894}\approx .003356$