Question

A forest contains about 700 trees. You randomly choose 65 trees and find that 30 of them are pine trees. What is the probability that a randomly selected tree will be a pine tree? Is this probability theoretical or experimental?

(1 point)
Responses

start fraction 65 over 700 end fraction approximately equals 9%; experimental
Image with alt text: start fraction 65 over 700 end fraction approximately equals 9% ; experimental

start fraction 30 over 65 end fraction approximately equals 47%; experimental
Image with alt text: start fraction 30 over 65 end fraction approximately equals 47% ; experimental

start fraction 30 over 65 end fraction approximately equals 46%; theoretical
Image with alt text: start fraction 30 over 65 end fraction approximately equals 46% ; theoretical

start fraction 30 over 65 end fraction approximately equals 46%; theoretical

Answer 1

To find the probability that a randomly selected tree will be a pine tree based on your sample, you can use the formula for probability:

\[
P(\text{Pine tree}) = \frac{\text{Number of pine trees in sample}}{\text{Total number of trees in sample}}
\]

In your case, you found that 30 out of the 65 trees you selected are pine trees.

\[
P(\text{Pine tree}) = \frac{30}{65} \approx 0.4615
\]

This means the probability is approximately 46%.

Now, whether this probability is theoretical or experimental depends on the context of how it was derived:

- **Theoretical probability** is based on expected outcomes in a perfect model, usually calculated based on total populations or uniform distributions.
- **Experimental probability** is based on actual results from experiments or trials.

Since you calculated this probability from a sample of trees that you actually selected, it is considered **experimental probability**.

Thus, the correct response is:

**start fraction 30 over 65 end fraction approximately equals 46%; experimental**