Given the results from rolling the 8-sided die 15 times:
[tex]\[ \{3, 4, 5, 2, 7, 1, 3, 7, 2, 6, 2, 1, 7, 3, 6\} \][/tex]
1. Determine the number of times an odd number was rolled:
The odd numbers in the specified results are: 3, 5, 7, 1, 3, 7, 1, 7, 3.
Thus, an odd number was rolled 9 times.
2. Calculate the total number of rolls:
The die was rolled a total of 15 times.
3. Find the experimental probability of rolling an odd number:
[tex]\[ \text{Experimental Probability} = \left( \frac{\text{number of odd results}}{\text{total number of rolls}} \right) \times 100 \][/tex]
[tex]\[ \text{Experimental Probability} = \left( \frac{9}{15} \right) \times 100 = 60\% \][/tex]
4. Determine the theoretical probability of rolling an odd number on an 8-sided die:
Since the die is marked with numbers 1 to 8, the odd numbers are 1, 3, 5, and 7. Thus, there are 4 odd numbers out of 8 possible numbers.
[tex]\[ \text{Theoretical Probability} = \left( \frac{\text{number of odd numbers}}{\text{total numbers on the die}} \right) \times 100 \][/tex]
[tex]\[ \text{Theoretical Probability} = \left( \frac{4}{8} \right) \times 100 = 50\% \][/tex]
5. Calculate the difference between the experimental and theoretical probabilities:
[tex]\[ \text{Difference} = \text{Experimental Probability} - \text{Theoretical Probability} \][/tex]
[tex]\[ \text{Difference} = 60\% - 50\% = 10\% \][/tex]
Therefore:
The experimental probability of rolling an odd number is [tex]\(60\%\)[/tex], which is [tex]\(10\%\)[/tex] more than the theoretical probability.
