Step 1: Convert to a common counting model:
Think of the sample space as split into 13 equal parts, since every probability given has denominator 13.
So A occupies 7 parts, B occupies 9 parts, and the overlap A and B occupies 4 parts, out of 13 total parts.
Step 2: Count the union using a part diagram:
Parts only in A (not B) = $7-4=3$. Parts only in B (not A) = $9-4=5$. Parts in both = $4$.
Adding these disjoint counts gives the union count:
\[ \text{Union parts} = 3+5+4 = 12 \]
So $P(A\cup B) = \dfrac{12}{13}$, matching the addition rule result.
Step 3: Find conditional probability using the part model:
Given that B has occurred means we restrict attention to the 9 parts that make up B.
Out of these 9 parts, only the overlap part, which is 4 parts, also belongs to A.
Step 4: Compute the ratio:
\[ P(A/B) = \frac{\text{parts in both A and B}}{\text{parts in B}} = \frac{4}{9} \]
This confirms the same answer using a counting argument instead of direct formula substitution.
Final Answer:
Both values match the formula based calculation.
\[ \boxed{P(A\cup B)=\frac{12}{13}, \quad P(A/B)=\frac{4}{9}} \]