Thread: probability question, not sure how to write this equation out.

1. probability question, not sure how to write this equation out.

Suppose that the probability of a person having a headache is 0.01, that the probability of a person having a fever given that the person has a headache is 0.4, and that the probability of a person having a fever is 0.02. Find the probability that a person has a headache given that the person has a fever.

2. Re: probability question, not sure how to write this equation out.

Here's how I would do that: Imagine 10000 people. 0.01 of them, or 100, have a headache. 0.04 of those people, or 4, have fever. But we also know that 0.02 of the original 10000, or 200, have a fever. So 4 of the 200 people with a fever also have a headache. Given that person has a fever, there is a 4/200= .02 probability they also have a headache.

3. Re: probability question, not sure how to write this equation out.

Given: $\displaystyle \mathcal{P}(H)=.01,~\mathcal{P}(F)=.02,~\& ~\mathcal{P}(F|H)=.04$.
You want to find $\displaystyle \mathcal{P}(H|F)=\frac{\mathcal{P}(H\cap F)}{\mathcal{P}(F)}$,
So to do that, you need to know $\displaystyle \mathcal{P}(H\cap F)$.