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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}{c}
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.

Sagot :

GinnyAnswer
To answer the question, "Assuming someone has a flower garden, what is the probability they also have a vegetable garden?" we need to use Table B.

Here’s the detailed, step-by-step solution:

1. Understand the Given Problem: We are given a condition that the person has a flower garden, and we need to find the probability that they also have a vegetable garden given this condition.

2. Identify the Relevant Probabilities from Table B:
- We are given the probabilities of different garden types based on whether there is a flower garden or not.
- Specifically, we need the probabilities associated with having a Flower Garden.

3. Determine the Total Probability of Having a Flower Garden:
- From Table B, the total probability of having a Flower Garden is given as 1.0. This value comes from summing the probabilities in the row corresponding to Flower Garden.

4. Determine the Joint Probability of Having Both a Flower Garden and a Vegetable Garden:
- From Table B, the joint probability of having both a Flower Garden and a Vegetable Garden is given as 0.56.

5. Use Conditional Probability Formula:
- To find the probability of having a Vegetable Garden given that there is a Flower Garden, use the conditional probability formula:
[tex]\[ P(\text{Vegetable Garden}|\text{Flower Garden}) = \frac{P(\text{Vegetable Garden and Flower Garden})}{P(\text{Flower Garden})} \][/tex]
- Substitute the known values:
[tex]\[ P(\text{Vegetable Garden}|\text{Flower Garden}) = \frac{0.56}{1.0} \][/tex]

6. Perform the Calculation:
- Simplifying the fraction gives:
[tex]\[ P(\text{Vegetable Garden}|\text{Flower Garden}) = 0.56 \][/tex]

Therefore, the probability that someone has a vegetable garden given that they have a flower garden is 0.56 or 56%.

Conclusion:
To answer the question, "Assuming someone has a flower garden, what is the probability they also have a vegetable garden?", we look at Table B because the condition provided is the presence of a flower garden. Thus, the answer is clearly:

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