Also, I think you'll have a lot less counting to do if you start from the other side. The cases are:
5 hits (auto-death, crits or defense doesn't matter) = 0.7 ^ 5
4 hits with crit (auto-death, defense doesn't matter) = (0.7 ^ 4 * 0.3 * 5) * (1 - (5/7)^4)
4 hits without crit, fail on defense = (0.7 ^ 4 * 0.3 * 5) * ((5/7)^4) * 0.3
That's without counting rerolls. 46.2595%. I'd estimate the full odds of double killing pets is about 25-30% at best.
"The beatings will continue until morale has improved."
- Standard corporate management technique