I don't understand what the issue is. The client wants you to plan for disaster, and they aren't math oriented, so asking for 100% probability sounds reasonable. The engineer, as engineers are prone to do, remembered his first day of prob&stat 101, without considering that the client might not. When they say this, they aren't thinking about nuclear winter, they are thinking about Fred dumping his coffee on the office…
Maybe it would be good to write the custom an email explaining stuff like 99%=Well run server 99.9%=Multiple backups, will cover most hardware failures 99.99%=Top grade commercial 99.999%=What companies like Google or Yahoo can achieve 99.9999%=Hopefully the US strategic defense systems are this reliable Also, you're assumption about the servers are entirely independant. That's a reasonable assumption in terms of fir…
Even worse. Five nines is five minutes of downtime per year. The core Google search experience blew five nines for half a decade with just one outage -- the one where they marked the entire Internet as a malware site, which took somewhere like 40 minutes to address.
This kind of thing makes me dismiss talk of nines as fetishism or sales-speak. You can say your system is going to have five nines of uptime at the application level. You're probably lying.
P.S. Pricing-wise, a client who wants > 99.5% either wants to pay mid-six figures (and up up up) or they want something which is deeply irrational for you to offer.