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.
