I hope to calculate $P(X+Y>0 \ |\ Y<0)$, where $X$, $Y$ are independent normal distribution with same mean ($\mu$) and variance ($\sigma$).
I tried to do it with direct integration. That is calculate $P(X+Y>0 \textrm{ and } Y<0)$ first. But failed after I eliminate the first integration sign.
Any other method to calculate this probability?