Let's determine the required probabilities step-by-step:
1. Identify the odd numbers and their occurrences:
The die has the numbers 1 to 8. The odd numbers in this range are 1, 3, 5, and 7.
2. Count the number of rolls and the number of times an odd number was rolled:
The results of the 15 rolls are: 3, 4, 5, 2, 7, 1, 3, 7, 2, 6, 2, 1, 7, 3, 6.
Based on these results:
- 3 is rolled 3 times.
- 5 is rolled 1 time.
- 7 is rolled 3 times.
- 1 is rolled 2 times.
Total occurrences of odd numbers: [tex]\(3 (3's) + 1 (5's) + 3 (7's) + 2 (1's) = 9\)[/tex] times.
3. Calculate the experimental probability:
Experimental Probability = [tex]\(\frac{\text{Number of times an odd number is rolled}}{\text{Total number of rolls}} \times 100\%\)[/tex]
[tex]\[
\frac{9}{15} \times 100\% = \frac{3}{5} \times 100\% = 60\%
\][/tex]
4. Determine the theoretical probability:
A fair 8-sided die has 4 odd numbers out of 8 numbers.
Theoretical Probability = [tex]\(\frac{\text{Number of odd sides}}{\text{Total number of sides}} \times 100\%\)[/tex]
[tex]\[
\frac{4}{8} \times 100\% = \frac{1}{2} \times 100\% = 50\%
\][/tex]
5. Calculate the difference between the experimental and theoretical probabilities:
Difference = Experimental Probability - Theoretical Probability
[tex]\[
60\% - 50\% = 10\%
\][/tex]
So, the experimental probability of rolling an odd number is 60%, which is 10% more than the theoretical probability.
