Comment Re:Ah, well, that lets Microsoft off the hook then (Score 1) 323
Still it means that the chance to be infected provided you know what you're doing is 1/10th of that if you don't.
No it doesn't. It means that for every 100 machine infected, 1/10 were belonging to those who knew what they were doing. In fact, it is actually possible (and likely given that it appears that most people do not know what they're doing [with Windows]) that you're chance of being infected if you know what you're doing is GREATER than if you don't know what you're doing!
Only if the NUMBER of machines owned by people who know what they're doing EQUALS the NUMBER of machines owned by people who don't know what they're doing will it mean you've got a 1/10 of the chance of being infected if you know what you are doing vs no knowing which means that the chance you've got of being infected if you know what you're doing is 1/9 that if you don't., since 1/9 of 9/10 is 1/10. Here's why:
<nerd mode>
The chance of being infected is
Pr(infected) = Pr(I) = <number of machines infected> / <total number of machines>
Pf(knowing) = Pr(K) = <number of machines of those knowing> / <total number of machines>
Pf(not knowing) = Pr(nK) = <number of machines of those not knowing> / <total number of machines>
also
Pr(infected | not knowing) = Pr(I | nK) = <number of infected of not knowing> / <total number of not knowing>
and
Pr(infected | knowing) = Pr(I | K) = <number of infected knowing> / <total number of knowing>
However, all we know is
Pr(knowing | infected) = Pr(K | I) = <number of infected knowing> / <total number of infected> = 1/10
Pr(not knowing | infected) = Pr(nK | I) = <number of infected not knowing> / <total number of infected> = 9/10
but we can use
Pr(I | K) = Pr(K | I) * P(I) / Pr(K)
similarly for
pr(I | nK) = Pr(nK | I) * P(I) / Pr(nK)
Then the chance to be infected provided you know what you're doing against that if you don't. is...what? I'll assume that it means how much more likely you are to be infected given you know what you're doing vs if you don't, ie
ch(K vs nk) = Pr(I | K) / Pr(I / nK)
ch(K vs nK) = Pr = Pr(K | I) * P(I) / Pr(K) / (Pr(nK | I) * P(I) / Pr(nK))
ch(K vs nK) = Pr(K | I) * P(I) * Pr(nK) / (Pr(nK | I) * Pr(I) *Pr(K))
ch(K vs nK) = Pr(K | I) * Pr(nK) / (Pr(nK | I) * Pr(K))
ch(K vs nK) = 1/10 * Pr(nK) / (9/10 * Pr(K))
ch(K vs nK) = 1/9 * (Pr(nK) / Pr(K))
I suspect that the majority of Windows users do not know what they're doing, thus: Pr(nK) > Pr(K) meaning that Pr(nK) / Pr(K) > 1 and ch(K vs nK) = (1/9 * [> 1]) > 1/9.
In particular, if the number of those who don't know what they're are doing (as I guess most people would suspect) is such that there are more than 9 times those who do know what they're doing, then
Pr(K) = #(K) / (#(K) + #(nK)) = #(K) / (#(K) + (9+d)#(K)) = #(K) / (#(K)(9+d)) = 1/(10+d) < 1/10
Pr(nK) = 1 - Pr(K) > 9/10
then the chance of being infected knowing vs not knowing is
ch(K vs nK) = 1/9 * ((9+d)/(10+d)) / (1/(10+d)) = 1/9 * (9+d) / 1 = 1/9 * (9+d) = 1 + d/9 > 1
meaning that you're MORE likely to be infected if you KNOW what you're doing then if you DON'T!
</nerd mode>