jmc

For the sum to be even, the two selected numbers must have the same parity (must be either odd and odd or even and even). The first spinner has $2$ odd numbers and $2$ even, so no matter what the second spinner is, there is a $1/2$ chance the first spinner lands on a number with the same parity, so the probability of an even sum is $1/2\to \boxed{\frac{1}{2}}$.