Question

A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres, nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A tree is chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probability that the tree is not within the acres of apple trees?

25.0%
37.5%
62.5%
75.4%

Answer 1

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.

1. **Total Acres of the Orchard**: 40 acres
2. **Acres with Apple Trees**: 25 acres
3. **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.

4. **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:

\[
P(\text{not apple}) = \frac{\text{Acres without apple trees}}{\text{Total acres}} = \frac{15}{40}
\]

5. **Simplifying the Probability**:
\[
P(\text{not apple}) = \frac{15}{40} = \frac{3}{8}
\]

6. **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%**