To find the theoretical probability that a tree chosen at random is not within the acres of apple trees, we first need to determine the total number of acres planted with trees and the number of acres not planted with apple trees.
- Total Acres of the Orchard: 40 acres
- Acres with Apple Trees: 25 acres
- Acres without Apple Trees: Total acres - Acres with Apple Trees = 40 acres - 25 acres = 15 acres
Next, we can find the probability that a randomly chosen tree is not within the acres of apple trees.
- Probability Calculation:
- Total acres without apple trees = 15 acres
- Total acres = 40 acres
The probability that the tree is not an apple tree is given by:
\[ P(\text{not apple}) = \frac{\text{Acres without apple trees}}{\text{Total acres}} = \frac{15}{40} \]
-
Simplifying the Probability: \[ P(\text{not apple}) = \frac{15}{40} = \frac{3}{8} \]
-
Converting to Percentage: To convert the fraction to a percentage, we do the following calculation:
\[ P(\text{not apple}) = \frac{3}{8} \times 100% = 37.5% \]
Thus, rounded to the nearest tenth of a percent, the theoretical probability that a tree is not within the acres of apple trees is 37.5%.
The correct answer is:
37.5%