Question

Determine the percentage of farmers with Rocky soil who prefer producing carrots
Carrots. Peppers. Totals
Sandy soil. 120. 50. 170
Rocky soil. 100. 150. 250
Totals. 220. 200. 420
Using relative frequencies, what is the percentage chance that if a farmer prefers to grow carrots they have Rocky soil

Answer 1

To determine the percentage of farmers with Rocky soil who prefer producing carrots, we need to calculate the proportion of farmers with Rocky soil who choose carrots compared to the total number of farmers with Rocky soil.

1. **Extract the relevant numbers from the table:**
- Total farmers with Rocky soil: 250
- Farmers with Rocky soil who prefer carrots: 100

2. **Calculate the percentage of farmers with Rocky soil who prefer carrots:**
\[
\text{Percentage} = \left(\frac{\text{Number of Rocky soil farmers who prefer carrots}}{\text{Total number of Rocky soil farmers}}\right) \times 100
\]
\[
\text{Percentage} = \left(\frac{100}{250}\right) \times 100 = 40\%
\]

Thus, **40%** of the farmers with Rocky soil prefer producing carrots.

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Now, to find the percentage chance that if a farmer prefers to grow carrots they have Rocky soil, we proceed as follows:

1. **Total number of farmers who prefer carrots:** 220 (from the totals row)
2. **Farmers who prefer carrots and have Rocky soil:** 100

3. **Calculate the probability that a farmer who prefers carrots has Rocky soil:**
\[
\text{Percentage} = \left(\frac{\text{Number of farmers with Rocky soil who prefer carrots}}{\text{Total number of farmers who prefer carrots}}\right) \times 100
\]
\[
\text{Percentage} = \left(\frac{100}{220}\right) \times 100 \approx 45.45\%
\]

Therefore, the percentage chance that if a farmer prefers to grow carrots, they have Rocky soil is approximately **45.45%**.