A(n) __________ summarizes how risk management will be perfomed on

In orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any given A and B, an event X which satisfies P(X) = P(B|A). Later extended by others, this result stands as a major obstacle to any talk about logical objects that can be the bearers of conditional probabilities.
I'm aware that in Bayesian analysis, the conditional likelihood P(B|A) is not a probability distribution. There must be a connection here right? What are some simple examples of conditional events that are not in the event algebra?

Describe the two basic functions of the qualitative risk analysis process and explain why a project manager should perform a qualitative risk analysis prior to quantitative risk analysis.

__________ involves prioritizing risks based on their probability and impact ofoccurrence.
Qualitative risk analysis
Risk response planning
Quantitative risk analysis
Risk management planning

I'm trying to understand the functional form of the Generalized Pareto distribution (GPD). In the "Definition" section location parameter μ does not appear in the function, whilst in the "Characterization" section it does.
1. how the GPD form can be reconciled with GPD form presented in other sources. Derivation of the GPD from the Generalized Extreme Value (GEV) distribution would suggest that $\frac{x-\mu }{\sigma }$ should not appear in that form in the expression of the GPD.

how are the two definitions related?
function definitions
$u(x)$: this functions takes in a vector $x\in R^n$ and spits out a value $u(x)\in R$
$r(x)=\frac{-u^{″}(x)}{u^{\prime }(x)}$ (risk coefficient)
$k(x)=\frac{|u^{\prime }(x)|}{(1+(u^{\prime }(x){)}^2{)}^{3/2}}$
In class, we've been using utility functions that have a constant absolute risk version coefficient. This function is:
$u(x)=(\frac{4}{3})(1-(1/2{)}^{x/50})$
Thus, $u^{\prime }(x)=\frac{-(2\ast (1/2{)}^{x/50}\ln (1/2))}{75}$
$u^{″}(x)=\frac{-((1/2{)}^{x/50}log(1/2{)}^2}{1875}$
And we have:
$r(x)=\frac{-\ln (1/2)}{50}$
However, curvature is:
$k(x)=\frac{1}{((4(\frac{1}{2}{)}^{x/25}\frac{log(1/2{)}^2}{5625}+1{)}^{3/2}}=\frac{1}{(.00034166(\frac{1}{2}{)}^{x/50}+1{)}^{3/2}}$
So, clearly this line does not have constant curvature by the geometric definition. This is also obvious when looking at a graph of $u(x)$. So, I'm struggling to relate the two measures. Is Arrow-Pratt discussing the relationship between slope and curvature?

There are 3 lottery tickets one can choose from:
$\begin{array}{|rrr|}\hline Alternatives& Chances& Outcome\\ A& 1/1000& \$1000\\ & 999/1000& \$0\\ B& 1/100& \$100\\ & 99/100& \$0\\ C& 1/2000& \$1000\\ & 1/200& \$100\\ & 1989/2000& \$0\\ \hline\end{array}$
And the formula for computing the probabilities of final outcomes when a coin is flipped between lotteries $A\mathrm{\&}B$ yields
$P_{\$1000}=\frac{1}{2}\frac{2}{2000}=\frac{1}{2000}$
$P_{\$100}=\frac{1}{2}\frac{20}{1000}=\frac{10}{1000}$
$P_{00}=1-P_{\$1000}-P_{\$100}$
$=\frac{1989}{2000}$
So there are 3 different probabilities here. The first one, $P_{\$1000}$ is the probability of the outcome being $1000$ dollars, which is (the probability of getting lottery A from the coin flip) x (the probability of the outcome being $1000$ dollars). That makes sense from the table above. But the second one, $P_{\$100}$, the probability of the outcome being $100$ dollars should be $\frac{20}{2000}$ or $\frac{1}{100}$. Why then is it $\frac{20}{1000}$???

Describe the risk analysis approach and the steps in a detailed or formal risk analysis