Your math is off. The actual chance assuming they're each independent is 42.1%. I'm usure how much the assumption they're independent holds up in this case.

Modern nuclear missiles (from the US, Russia, and China at least) are all MIRV[1] designs. Each missile might contain, as an example, 10 independent micro-warheads each capable of mass casualties. That means for every single offensive missile fired, the defender has to be 100% effective at countering 10 separate threats.

[1] https://en.wikipedia.org/wiki/Multiple_independently_targeta...

This calculation only holds if the failures are random, not if the missiles exploit some weakness in the system to get through.