To determine the value for [tex]\( a \)[/tex] that completes the conditional relative frequency table by row, we need to follow these steps:
1. Review the given data:
- Fiction row:
- Poetry: 0.2
- Prose: 0.8
- Total: 1.0
- Non-Fiction row:
- Poetry: [tex]\( a \)[/tex]
- Prose: 0.9
- Total: 1.0
- Total row:
- Poetry: 0.18
- Prose: 0.82
- Total: 1.0
2. Focus on the Non-Fiction row. We know the total for Non-Fiction is 1.0, and within that, the proportion of Prose is 0.9. Hence, the proportion of Poetry (denoted as [tex]\( a \)[/tex]) can be found by subtracting the proportion of Prose from the total:
[tex]\[
a = \text{Total Non-Fiction} - \text{Prose Non-Fiction}
\][/tex]
Given the total for Non-Fiction is 1.0 and the Prose Non-Fiction is 0.9:
[tex]\[
a = 1.0 - 0.9
\][/tex]
3. Perform the subtraction:
[tex]\[
a = 0.1
\][/tex]
Thus, the value of [tex]\( a \)[/tex] that completes the table is:
[tex]\[
a = 0.1
\][/tex]
Hence, the correct choice from the given options is:
[tex]\[
0.1
\][/tex]
