To determine the theoretical probability that a slip of paper chosen from a hat containing slips numbered 1 to 15 will be an even number, let's follow a step-by-step approach.
1. Identify the Total Number of Possible Outcomes:
- The slips are numbered from 1 to 15. Therefore, there are 15 possible outcomes in total.
2. Determine the Favorable Outcomes:
- These are the slips that have even numbers. The even numbers between 1 and 15 are: 2, 4, 6, 8, 10, 12, and 14.
3. Count the Number of Favorable Outcomes:
- The count of these even numbers is 7.
4. Calculate the Theoretical Probability:
- Probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
- Therefore, the probability [tex]\( P \)[/tex] that a slip chosen at random will be an even number is:
[tex]\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{7}{15}
\][/tex]
So, the theoretical probability that a slip of paper chosen will be an even number is:
[tex]\[
\boxed{\frac{7}{15}}
\][/tex]
