Question

A farmer grows vegetables on seven acres, fruit on six acres, and flowers on two acres. Out in his fields, he finds a ladybug.

To the nearest tenth of a percent, what is the theoretical probability that the ladybug was not found within the acres of flowers?

13.3%
15.4%
84.6%
86.7%

Answer 1

To find the theoretical probability that the ladybug was not found within the acres of flowers, we first need to determine the total area of the farmer's fields and the area designated for flowers.

1. Calculate the total area of the fields:
- Vegetables: 7 acres
- Fruit: 6 acres
- Flowers: 2 acres

Total area = 7 acres + 6 acres + 2 acres = 15 acres

2. Calculate the area that is not designated for flowers:
- Total area - Area of flowers = 15 acres - 2 acres = 13 acres

3. Calculate the probability that the ladybug was not found within the flowers:
\[
\text{Probability (not in flowers)} = \frac{\text{Area not in flowers}}{\text{Total area}} = \frac{13 \text{ acres}}{15 \text{ acres}}
\]

4. Convert the probability to a percentage:
\[
\text{Probability (not in flowers)} = \frac{13}{15} \approx 0.8667
\]
\[
0.8667 \times 100 \approx 86.67\%
\]

5. Rounding to the nearest tenth of a percent, we find that the probability is approximately **86.7%**.

Thus, the answer is **86.7%**.