To determine the theoretical probability of drawing an even-numbered slip from a hat containing slips numbered from 1 to 15, we can proceed with the following steps:
1. Identify Total Number of Slips: First, we note there are slips numbered from 1 to 15. Therefore, the total number of slips in the hat is 15.
2. List of Even Numbers: Next, we identify the even numbers between 1 and 15. These even numbers are:
[tex]\[
2, 4, 6, 8, 10, 12, 14
\][/tex]
Thus, there are 7 even-numbered slips.
3. Calculate the Number of Even Slips: We count the number of even slips, which are 7 in total.
4. Determine the Probability: The probability of drawing one of these even-numbered slips is given by the ratio of the number of favorable outcomes (the even-numbered slips) to the total number of possible outcomes (all the slips). Therefore, the probability [tex]\( P \)[/tex] is:
[tex]\[
P = \frac{\text{Number of even slips}}{\text{Total number of slips}} = \frac{7}{15}
\][/tex]
So, the theoretical probability that a slip of paper chosen will be an even number is [tex]\( \frac{7}{15} \)[/tex].
The correct choice from the given options is:
[tex]\[
\boxed{\frac{7}{15}}
\][/tex]
