To find the theoretical probability that a slip of paper chosen from a hat numbered from 1 to 15 will be an even number, we can follow these steps:
1. Identify the Total Number of Slips:
The total number of slips is from 1 to 15, so there are 15 slips in total.
2. Determine the Number of Even Numbers Between 1 and 15:
We list all the numbers in this range and identify which ones are even:
- 2, 4, 6, 8, 10, 12, 14
Counting these, we see that there are 7 even numbers.
3. Calculate the Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
So, the probability [tex]\( P \)[/tex] of drawing an even-numbered slip is:
[tex]\[
P(\text{even number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{7}{15}
\][/tex]
4. Convert to Decimal Form (for clearer understanding as needed):
This fraction can be converted to a decimal to aid in better understanding:
[tex]\[
\frac{7}{15} \approx 0.4667
\][/tex]
Therefore, the theoretical probability that a slip of paper chosen will be an even number is [tex]\(\frac{7}{15}\)[/tex], which is approximately 0.4667 or 46.67%.
The correct answer is not among the ones provided. However, based on our calculations, it is clear the chance of picking an even number from the slips labeled 1 to 15 is [tex]\(\frac{7}{15}\)[/tex].
