Probability of "manmade global warming is a problem with solutions that are cost-effective" I came across this post from a climate change skeptic, which made the following point (emphasis mine):

However, if Pope Francis is right that history will judge us, we need to decide what, if any, action is called for by asking four questions: Is the earth warming? Is that an overall bad thing? Is human activity the primary cause? And would forced standards be cost-effective?
Regrettably, none of those questions can be answered with absolute confidence because our knowledge is limited by data, finite in number and dependent on processes that, in some cases, are not fully known and, in others, not even identified. As already discussed, answering the first question and most basic with any degree of confidence is unlikely.
Yet even if each of those questions could be answered in the affirmative with 80 percent probability, their cumulative probability would be 41 percent, indicating the proposition that “manmade global warming is a problem with solutions that are cost-effective” is, at best, problematic.

I get the calculation ($0.8^4=0.4096 \approx 41\%$). However, I feel there is something wrong here. The above calculation seems to assume the answers are entirely independent. But they are clearly not. For example, if the Earth is not warming, then this is clearly not a bad thing, nor there is a cause to nothing, so humans cannot be such cause to nothing. Therefore, the first question kind of makes the other three redundant.
Similarly, if human activity is the cause of global warming, a cost-effective solution is more likely to exist that if global warming is not due to human actions. Thus, there last question is not independent of the other either.
How would one go to properly address this problem then? Do we need complete information of the joint distribution of the answers to the four questions?
 A: I usually parse such arguments as involving conditional probabilities
$\Pr(A,B,C,D) = \Pr(D|C,B,A) \Pr(C|B,A) \Pr(B|A) \Pr(A)$
which is formally correct without any assumptions of independence. (Rather like the Drake equation.)
Formal correctness doesn't make up for vagueness in the definitions of the events†, or for our being expected to nod along with numbers pulled out of thin air:—"80%'s quite a good chance, he's being fair there, isn't he?".&ddagger; A cynical reader might suppose that an intial description of the outcome as a conjunction of affirmative answers to three questions (each with a generous-sounding 80% probability) didn't yield a low enough joint probability to make the point.
† Which isn't the only reason these "yes/no" questions would surely better be posed as "how much" questions.
&ddagger; Moreover, as @gung points out, we're entitled to some explanation of the concept of probability being used here, presumably one quantifying degree of belief rather than long-run frequency.
