To answer the question "Assuming someone has a flower garden, what is the probability they also have a vegetable garden?", we can use information provided in the second table (Table B). Let’s break down the process step by step.
1. Calculate the Probability of Having a Flower Garden (P(Flower)):
[tex]\[
P(\text{Flower}) = \frac{\text{Total number of Flower Gardens}}{\text{Total number of Gardens}}
\][/tex]
According to Table B:
[tex]\[
P(\text{Flower}) = \frac{10}{20} = 0.5
\][/tex]
2. Identify the Joint Probability of Having Both Vegetable and Flower Gardens (P(Vegetable and Flower)):
From Table B, the probability for Vegetable and Flower Garden together is given as:
[tex]\[
P(\text{Vegetable and Flower}) = 0.56
\][/tex]
3. Apply Conditional Probability Formula:
The conditional probability formula states:
[tex]\[
P(\text{Vegetable}|\text{Flower}) = \frac{P(\text{Vegetable and Flower})}{P(\text{Flower})}
\][/tex]
4. Plug in the values:
[tex]\[
P(\text{Vegetable}|\text{Flower}) = \frac{0.56}{0.5} = 1.12
\][/tex]
Thus, the probability that someone with a flower garden also has a vegetable garden is 1.12. This value indicates some form of dependency or error in the provided data, but for the question given, this is the direct result.
