I searched several links within this site and came upon many questions regarding the sum of two variables, but haven't been able to find a question regarding three.
Here is the question I came across in my book:
"Three points $A$,$B$ and $C$ are selected at random from the interval $(8,12)$.
Find the probability that $A<B<C$.
The question didn't specify, but after researching, and looking at the chapter heading, I am assuming that $A$,$B$, and $C$ are independent and uniformly distributed.
I am assuming that based on this.
The visualization I originally came up with was like so:
$|(-8)-----A-----B-----C-----(12)|$
Then, I set up my integral as:
$\frac1{20^3}\int_{-8}^{12} \int_{A}^{12} \int_{B}^{12}1 \,dC\,dB\,dA$ =$\frac16$
However, I'm not sure if that's correct.
A lot of other, similar, problems start graphing on an X, Y plane, so I am skeptical of my answer.
Like, I'm not sure if I should write it as a conditional probability either, such as $P(A<B<C)=P(B<C|A<B)$ or something similar.
I guess I am having trouble visualizing this problem with confidence and other, similar problems, and I would appreciate any and all clarifications! Thank you!