David Yom, Miracles and Induction

I read in a book by a Christian fan David Hume’s argument against miracles. Hume claims that we have already seen a perfectly healthy person who suddenly died. It is rare, but it has been observed, and therefore it is not a miracle. On the other hand, we have never seen a dead person resurrected (he could have been less transparent in his criticism of the New Testament, but he did) and therefore the argument against miracles is as strong as any argument we have from observation.
Apparently I’m not understanding something very basic in Hume’s doctrine. Wasn’t he the one who talked about the problem of induction? Doesn’t the problem of induction undermine the above argument against miracles?