Let's say that I have $3$ random normal variables, $A$, $B$ and $C$.
They all have a standard deviation of $17.526$, while $A$ has a mean of $143$, $B$ of $139$, and $C$ of $129$.
I want to calculate $P(A>C\mid A>B)$. I know how to calculate $P(A>C)$ and $P(A>B)$, but it's the conditional part I'm struggling with.
If it helps speed-wise, I have $P(A>C)$ to be $0.713912$, and $P(A>B)$ to be $0.564105$ with the difference distribution in each case having a stdev of $24.785$.
Thanks.