To find $A$ and $B$, let's follow these steps:

Step 1: Calculate $A$ (Observed Count for Blackwood in Category 1)

Since the total observed count for blackwood is 72, we can use this information to find $A$.

1. Sum of the observed counts for blackwood in all categories: $A + 15 + 17 + 18 = 72$
2. Solving for $A$: $A = 72 - (15 + 17 + 18) = 72 - 50 = 22$

Thus, $A = 22$.

Step 2: Calculate $B$ (Expected Count for Blackwood in Category 2)

The expected count in each cell is calculated by the formula: $\text{Expected Count} = \frac{(\text{Row Total}) \times (\text{Column Total})}{\text{Grand Total}}$

For $B$, the expected count for blackwood in category 2:

1. Row total for blackwood = 72
2. Column total for category 2 = 34
3. Grand total = 124

Then, $B = \frac{72 \times 34}{124} = \frac{2448}{124} = 19.742$

Thus, $B = 19.742$ (rounded to three decimal places).

Final Answer:

• A (Observed Count for Blackwood in Category 1): $22$
• B (Expected Count for Blackwood in Category 2): $19.742$