Sure, let's break down the steps to find the theoretical probability that a slip of paper drawn from a hat will be an even number, given that there are slips of paper numbered from 1 to 15 in the hat.
1. Determine the total number of slips:
There are slips numbered from 1 to 15, so the total number of slips is 15.
2. Identify the even numbers in the range 1 to 15:
The even numbers between 1 and 15 are: 2, 4, 6, 8, 10, 12, and 14.
3. Count the total number of even slips:
There are 7 even numbers in that range.
4. Calculate the theoretical probability of drawing an even slip:
Probability is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Here, the number of favorable outcomes (drawing an even slip) is 7, and the total number of slips is 15.
Therefore, the theoretical probability of drawing an even slip is:
[tex]\[
\frac{\text{Number of even slips}}{\text{Total number of slips}} = \frac{7}{15}.
\][/tex]
Thus, the correct answer is [tex]\(\frac{7}{15}\)[/tex].
