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The recent scare over Mad Cow disease has created the need for a new
test.  Mad Cow disease is very rare, and it affects 1 cow in a
million.  A new test is being marketed with the following properties.
\begin{itemize}
\item
If the cow has the disease, the test will always say the cow is infected.
\item
If the cow does not have the disease, the test will say the cow is
infected with probability $x$ (i.e. a false positive).
\end{itemize}

Let $p(x)$ be the probability the cow has the disease, given the test
says the cow is infected.  

Determine $p(x)$.  How small does $x$ have to be for $p(x)\geq\frac{1}{2}$?



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