Let's solve this problem step-by-step.
1. Identify the Total Number of Slips:
- There are slips numbered from 1 to 15. Therefore, the total number of slips is 15.
2. Identify the Even-Numbered Slips:
- The even numbers between 1 and 15 are: 2, 4, 6, 8, 10, 12, and 14.
- Counting these, we get 7 even-numbered slips.
3. Calculate the Theoretical Probability:
- Probability is defined as the ratio of the number of favorable outcomes (even-numbered slips) to the total number of outcomes (total slips).
- So, the probability [tex]\( P \)[/tex] is given by:
[tex]\[
P(\text{even number}) = \frac{\text{Number of even-numbered slips}}{\text{Total number of slips}} = \frac{7}{15}
\][/tex]
4. Conclusion:
- The theoretical probability of picking an even-numbered slip from the hat is [tex]\(\frac{7}{15}\)[/tex].
So, the correct answer is [tex]\(\boxed{\frac{7}{15}}\)[/tex].
