smc

The only time when $ad-bc$ is even is when $ad$ and $bc$ are of the same parity. The chance of $ad$ being odd is $\frac{1}{2}\cdot \frac{1}{2}=\frac{1}{4}$, since the only way to have $ad$ be odd is to have both $a$ and $d$ be odd. As a result, $ad$ has a $\frac{3}{4}$ probability of being even. $bc$ also has a $\frac{1}{4}$ chance of being odd and a $\frac{3}{4}$ chance of being even. Therefore, the probability that $ad-bc$ will be even is ${\left(\frac{1}{4}\right)}^2+{\left(\frac{3}{4}\right)}^2=\boxed{\frac{5}{8}}$.