By basic set theory, the intersection of two sets is a subset of their union:

By the monotonicity property of probability measures, if $A \subseteq B$, then $P(A) \le P(B)$.

When two dice are rolled simultaneously:
Total number of possible outcomes in sample space $S$ = $6 \times 6 = 36$.
Favourable outcomes where the sum of two dice equals 9:

Number of favourable outcomes $n(E) = 4$.

Probability:

By De Morgan's Law of set theory:

Applying the complement rule of probability:

By the addition theorem of probability:

Substituting into the complement equation:

Given:
$P(\overline{B}) = 1/2 \implies P(B) = 1 - 1/2 = 1/2$
From the addition rule of probability: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Now evaluate the product $P(A) \times P(B)$:

Since $P(A \cap B) = 1/3 = P(A) \cdot P(B)$, the events $A$ and $B$ satisfy the condition for statistical independence.