You are assuming that your client OS/browser DNS resolvers have the pre-shared trust anchors for whichever root zone. That's kind of a big assumption. :)
Without those, everything collapses, and even if they're there, you still might be in very real trouble and not even know it.
Scenario 1: best of all worlds: you're running an awesome mythical OS (edit: or browser plugin as jocluteseh mentioned below) with up to date root keys and you're trying to get to a single zone and you know the root zone key... but the DNSSEC root key was compromised. No one knew this, because there's no way to detect. Your MITM attacker just forges everything. But you feel secure, since you have DNSSEC. ;)
Scenario 2: you're running some really new fancy OS with a pre-shared DNSSEC root key and you make a query for DNSSEC for a zone that you don't have a key for. The recursor simply tells you that that zone doesn't have DNSSEC records. oops.
Scenario 3: you're running a current OS without any root zone anchors at all. You make a query to your preferred recursive DNS server (probably whatever you were handed via DHCP) and it just lies to you, about everything.
I don't understand your point about probabilities. In each of these scenarios, they're not a 1 in anything chance of getting owned in those circumstances.. that's a 1 in 1 chance. All it took was a MITM. To say nothing of the traffic analysis and complete lack of any sort of encryption for passive MITM's.