Hmm. Food for thought. Maybe strategic delay is in order.
We already have periodic backups, but they don’t solve the problem of losing email or whatnot in the interim. We know about putting DVDs in an offsite location for fire, etc. We don’t use tape, though. We had a tape drive circa 1999, and it was so loud and so slow that we abandoned it. Have they improved radically (other than capacity)?
Math check: if p is the probability of failure, it would seem the probability of no failure in n drives would be (1-p)^n – which should be less than 1-np. Right? Not much less for small values of p, though.
If you want to stay in the realm of math, the problem with this reasoning is that it assumes that the probability of failure of each drive is independent. Since they are sitting in the same place, in the same computer, with possibly the same design, that assumption does not hold. Things like fires and, I don’t know, flukey power supplies mean that certain failures can kill all your drives at once.