8. Let $A, B, C, D$ be four non-coplanar points in space, and connect an edge between each pair of points with a probability of $\frac{1}{2}$. Whether any two pairs of points are connected is independent of each other. Then the probability that $A$ and $B$ can be connected by (a single edge or a sequence of edges forming a) spatial polyline is $\qquad$ .
Answer: $\frac{3}{4}$.
Solution: There are 2 possibilities for whether an edge connects each pair of points, making a total of $2^{6}=64$ cases. Consider the number of cases where $A, B$ can be connected by a polyline.
(1) There is an $A B$ edge: There are a total of $2^{5}=32$ cases.
(2) There is no $A B$ edge, but there is a $C D$ edge: In this case, $A, B$ can be connected by a polyline if and only if $A$ is connected to at least one of $C, D$, and $B$ is connected to at least one of $C, D$. The number of such cases is $\left(2^{2}-1\right) \times\left(2^{2}-1\right)=9$.
(3) There is no $A B$ edge, and no $C D$ edge: In this case, there are $2^{2}$ ways for $A C, C B$ to be connected, and $2^{2}$ ways for $A D, D B$ to be connected, but the case where $A C, C B, A D, D B$ are all connected is counted twice, so the number of cases where $A, B$ can be connected by a polyline is $2^{2}+2^{2}-1=7$.
The total number of cases in the above three categories is $32+9+7=48$, so the probability that $A, B$ can be connected by a polyline is $\frac{48}{64}=\frac{3}{4}$.