Table B: Garden-Type Frequencies by Row

\begin{tabular}{|c|c|c|c|}
\cline { 2 - 4 }
\multicolumn{1}{c|}{} & \begin{tabular}{c}
Vegetable \\
Garden
\end{tabular} & \begin{tabular}{c}
No Vegetable \\
Garden
\end{tabular} & Total \\
\hline
\begin{tabular}{c}
Flower \\
Garden
\end{tabular} & 0.56 & 0.44 & 1.0 \\
\hline
\begin{tabular}{r}
No Flower \\
Garden
\end{tabular} & 0.48 & 0.52 & 1.0 \\
\hline
Total & 0.5 & 0.5 & 1.0 \\
\hline
\end{tabular}

Which table could be used to answer the question: "Assuming someone has a flower garden, what is the probability they also have a vegetable garden?"

A. Table A, because the given condition is that the person has a flower garden.
B. Table A, because the given condition is that the person has a vegetable garden.
C. Table B, because the given condition is that the person has a flower garden.
D. Table B, because the given condition is that the person has a vegetable garden.



Answer :

To determine which table can be used to answer the question "Assuming someone has a flower garden, what is the probability they also have a vegetable garden?" we need to understand the given condition and the information provided by the tables.

The condition in the question is that the person has a flower garden. Given this condition, we need to find the conditional probability that the person also has a vegetable garden.

The table we are provided with is Table B, which shows the frequencies of different types of gardens. Let's analyze the relevant data in Table B:

```
Table B: Garden-Type Frequencies by Row
------------------------------------------------
| | Vegetable Garden | No Vegetable Garden | Total |
------------------------------------------------
| Flower Garden | 0.56 | 0.44 | 1.0 |
------------------------------------------------
| No Flower | 0.48 | 0.52 | 1.0 |
| Garden | | | |
------------------------------------------------
| Total | 0.5 | 0.5 | 1.0 |
------------------------------------------------
```

From Table B, given that the person has a flower garden (which means we are in the row corresponding to "Flower Garden"), the total probability for the flower garden row is given as 1.0.

Within this row, the probability of having a vegetable garden is recorded as 0.56. Therefore, we can use this information to find the required conditional probability.

Hence, using the data from Table B and given the condition that the person has a flower garden:

The probability that they also have a vegetable garden is 0.56.

Thus, the correct answer to which table could be used for this question is:

Table B, because the given condition is that the person has a flower garden.