Question about various percentages to a 100%

Question

I see this notation in statistics

Lets say this is a report on cyber crime. They say damage is cost by various factors

Viruses $99\%$

Theft $55\%$

Direct attack $20\%$

Hactivism $72\%$

What I don't understand is, if total damage is $100\%$ how is this indiviual damaging elements calculated?

Answer 1

Let those represent sets: $$V,T,D,H$$ Note that $$V\cap T\ne\phi,T\cap D\ne\phi\cdots$$

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Those sets are not disjoint. A computer may be affected by virus and theft both or even some three factors, as the question suggests.

Answer 2

Many (I would be tempted to say $90\%$) of the conversions to percentages in the press are wrong. It looks like you are combining percentages from the seventh slide (as best I can tell) of the linked presentation. In this case, there is nothing to indicate that one attack cannot involve more than one of the factors. In that case, the factors can add up to more than $100\%$. I don't think it is clear at all what they are trying to say on that slide except to scare you and say there are many different attacks. If we change the percentages by $\pm 10\%$ what does that change? Nothing.

Answer 3

The events are not mutually exclusive.   Their measures may add to more than one because the intersections are not all zero.   More than one event can occur simultaneously.   They overlap.

$\begin{align}P(V \cup T\cup D\cup H) &= P(V)+P(T)+P(D)+P(H) \\ &\quad - P(V\cap T)- P(V\cap D)-P(V\cap H)-P(T\cap D)-P(T\cap H) - P(D\cap H) \\ & \quad + P(V\cap T\cap D)+ P(V\cap T\cap H)+ P(T\cap D\cap H) \\ & \quad - P(V \cap T\cap D\cap H)\end{align}$