10.78 Let i and j > i be arbitrary. Show that Pr [A<sub>i,j</sub>] = \frac{1}{2}.
10.79 Let i and j > i be arbitrary, and let i' and j' > i' be arbitrary. Show that any two distinct events A<sub>ij</sub> and A<sub>i'j'</sub> are independent. That
is, show that Pr [A<sub>ij</sub> | A<sub>i'j'</sub>] = Pr [A<sub>ij</sub>|\overline{A<sub>i'j'</sub>}] = \frac{1}{2} if {i,j} ? {i',j'}.
10.80 Show that there is a set of three distinct A events that are not mutually independent. That is, identify three events A<sub>i,j</sub>, A<sub>i'j'</sub>, and
A<sub>i''j''</sub> where the sets {i,j}, {i',j'}, and {i'', j''} are all different (though not necessarily disjoint). Then show that if you know the
value of A<sub>ij</sub> and A<sub>i'j'</sub>, the probability of A<sub>i''j''</sub> ? \frac{1}{2}.