Casework and Law of Total Probability

We have $3$ boxes of batteries. The number of good and dead batteries in each box are as follows:

Box $1$: $3$ good, $2$ dead

Box $2$: $4$ good, $1$ dead

Box $3$: $2$ good, $2$ dead

If we go over to the boxes, pick one of the boxes randomly, and pick a random battery out of that box, what is the probability that it is good?