Confusing term in total probability rule

Question

I'm working on the following probability problem:

I'm using Bayes' Rule and am having one problem. Using the total probability rule, the denominator of my Bayes' Rule expression looks like

$$ P(\text{fever | H1N1}) \cdot P(\text{H1N1}) + P(\text{fever | no H1N1}) \cdot P(\text{no H1N1}). $$

The first two and last terms are easy to gather from the information given. However, I'm having an issue figuring out how to compute $P(\text{fever | no H1N1})$. Would it just be 1% or is there a more complicated answer?

Answer 1

$P(\text{fever}|\text{no H1N1})$ is given in the sentence 'and $1\%$ of the people who have neither, have a high fever.' Note that you don't know for sure that somebody who doesn't have H1N1 doesn't have the flu, thus you should calculate this as $$ P(\text{fever}|\text{no H1N1, no flu})\cdot P(\text{no H1N1, no flu})+P(\text{fever}|\text{no H1N1, flu})\cdot P(\text{no H1N1, flu}) $$