Question

I read in a book by a Christian evangelist his presentation of David Hume’s claim against miracles. According to Hume, it has already happened that we have seen a completely healthy person suddenly die. True, that is rare, but it has been observed already, so it is not a miracle. On the other hand, we have never seen a dead person come back to life (he could have been a little less transparent in his criticism of the New Testament, but never mind), and therefore the argument against miracles is as strong as any argument we have from observation.
Apparently I’m missing something very basic in Hume’s thought. Isn’t he the one who talked about the problem of induction? Doesn’t the problem of induction undermine the above argument against miracles?