To find the theoretical probability that a slip of paper chosen at random from the ones numbered 1 to 15 will be an even number, we need to follow these steps:
1. Identify the total number of slips of paper: These slips are numbered from 1 to 15, so the total number of paper slips is 15.
2. Identify the even numbers from 1 to 15: These are the numbers divisible by 2.
- The even numbers are: 2, 4, 6, 8, 10, 12, and 14.
3. Count the total number of even slips of paper:
- From our list, the even slips are: 2, 4, 6, 8, 10, 12, and 14.
- There are 7 even numbers in total.
4. Compute the probability:
- Probability is calculated as the number of favorable outcomes divided by the total number of outcomes.
- Here, the number of favorable outcomes (even numbers) is 7.
- The total number of outcomes (total slips) is 15.
Therefore, the probability [tex]\( P \)[/tex] that a randomly chosen slip is an even number is given by:
[tex]\[
P(\text{even number}) = \frac{\text{number of even slips}}{\text{total number of slips}} = \frac{7}{15}
\][/tex]
Hence, the theoretical probability that a slip of paper chosen at random will be an even number is [tex]\( \frac{7}{15} \)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{\frac{7}{15}}
\][/tex]
