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Use the table to answer the question. Determining 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 Examine the data from a survey of farmers about their different soil types and the crops they prefer to grow. Using relative frequencies, what is the percentage chance that if a farmer prefers to grow carrots they have rocky soil? Round your answer to the nearest tenth. (1 point) Responses 100.0% 100.0% 40.0% 40.0% 83.3% 83.3% 45.5%

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To determine the percentage of farmers with rocky soil who prefer producing carrots, we first need to find the total number of farmers who prefer carrots and how many of them have rocky soil.

From the data:

  • Total farmers who prefer carrots = 220 (sandy soil: 120 + rocky soil: 100)
  • Total farmers with rocky soil = 250 (carrots: 100 + peppers: 150)

Now, we want to find the percentage of farmers with rocky soil who prefer carrots:

  1. Calculate the proportion of farmers with rocky soil who prefer carrots: \[ \text{Probability (Carrots | Rocky Soil)} = \frac{\text{Number of farmers with Rocky Soil preferring Carrots}}{\text{Total number of farmers with Rocky Soil}} = \frac{100}{250} \]

  2. Now calculate this fraction: \[ \frac{100}{250} = 0.4 \]

  3. To express this as a percentage, multiply by 100: \[ 0.4 \times 100 = 40.0% \]

Thus, the percentage chance that if a farmer prefers to grow carrots, they have rocky soil is 40.0%.