Find Probabilty of ~Fever

Question

I have been given this

P(Strep(some infection)) = 0.15    

P(fever|strep) = 0.6    

P(fever|~strep) = 0.3    

Find P(strep|fever) I could find this put by using bases rule. Bayes rule is
P(A/B) = P(B/A)*P(A) / P(B)

Here B is fever.

How do I find P(fever)?

Is it sum of P(fever|strep) and this P(fever|~strep)

If I can do this, and find P(~fever), I get it more than 1.

Where am I wrong?

Thank you

Answer 1

It is found as follows:

$$ P(\text{fever}) = P(\text{fever} \mid \text{strep}) P(\text{strep}) + P(\text{fever} \mid \neg\text{strep}) P(\neg\text{strep}) $$

where $\neg$ is the negation operator (I'm assuming that's what $\sim$ is in your question).