>
> Vendor A: 10% broken
> Vendor B: 10% broken
> P(both A and B broken):
> 10% x 10% = 1%
>
>Replacing your router (or firmware) almost always fixes your problem.
The conclusion is false :
if router A is broken, router B still have 10% chance to be broken, the two events being independant.
P(A broken | B broken) = 10%
To get the 1% effect, advice could be :
Always buy 2 routers instead of 1
If you have to replace the router, there's a 10% chance that new router is broken. But you only replace when the first router is broken, so it's 10% of 10%.
Read it as "a strategy of replacing when needed" rather than "replacing in all cases for the hell of it".
My (little) problem is the sentence "Replacing your router (or firmware) almost always fixes your problem.", because if the first router is broken, replacing it will only fix your problem in 10% of the cases, which is not "almost always".
I'm struggling to find a great way to put it. Maybe "a one-replacement backup plan gives you a 99% chance of success"? Close but not very elegant.
"Replacing your router (or firmware) fixes the problem except for 1% of all router buyers"?