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A survey of 126 farmers found that 72 of them planted carrots and 45 planted potatoes. There are 38 farmers that planted both carrots and potatoes, and 47 farmers that did not plant carrots or potatoes.

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
& Carrots & No Carrots & Total \\
\hline
Potatoes & & & \\
\hline
No Potatoes & & & \\
\hline
Total & & & \\
\hline
\end{tabular}
\][/tex]

Sagot :

GinnyAnsweridn
To determine the number of farmers in each category, we need to fill out the contingency table for the given data. Here's the detailed step-by-step solution:

### Step-by-Step Solution

1. Total Farmers: 126
2. Farmers Planted Carrots: 72
3. Farmers Planted Potatoes: 45
4. Farmers Planted Both Carrots and Potatoes: 38
5. Farmers Not Planted Either Carrots or Potatoes: 47

First, we need to calculate the number of farmers who planted only carrots, only potatoes, and either carrots or potatoes.

### Only Carrots:
Farmers who planted only carrots are those who planted carrots but not potatoes. We subtract the farmers who planted both from those who planted carrots:
[tex]\[ \text{Only Carrots} = \text{Farmers Planted Carrots} - \text{Farmers Planted Both} \][/tex]
[tex]\[ = 72 - 38 = 34 \][/tex]

### Only Potatoes:
Farmers who planted only potatoes are those who planted potatoes but not carrots. We subtract the farmers who planted both from those who planted potatoes:
[tex]\[ \text{Only Potatoes} = \text{Farmers Planted Potatoes} - \text{Farmers Planted Both} \][/tex]
[tex]\[ = 45 - 38 = 7 \][/tex]

### Either Carrots or Potatoes (or both):
To find the number of farmers who planted either carrots or potatoes or both, we subtract the farmers who did not plant either from the total number of farmers:
[tex]\[ \text{Planted Either} = \text{Total Farmers} - \text{Farmers Not Planted} \][/tex]
[tex]\[ = 126 - 47 = 79 \][/tex]

### Filling in the Table:
Using our calculated values, we can fill in the contingency table:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline & Carrots & No Carrots & Total \\ \hline Potatoes & 38 & 7 & 45 \\ \hline No Potatoes & 34 & 47 & 81 \\ \hline Total & 72 & 54 & 126 \\ \hline \end{tabular} \][/tex]

### Explanation for Each Box:
- Carrots + Potatoes (Top-Left): 38 (farmers who planted both)
- Carrots + No Potatoes (Bottom-Left): 34 (only carrots)
- No Carrots + Potatoes (Top-Right): 7 (only potatoes)
- No Carrots + No Potatoes (Bottom-Right): 47 (neither)

Summarizing, the contingency table provides a clear breakdown of the survey results, allowing us to understand the planting habits of the farmers.
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