Part A
To find the experimental probability of rolling a 6, we use the formula for experimental probability:
\[ \text{Experimental Probability} = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}} \]
In this case, the number of times a 6 was rolled is 32, and the total number of rolls is 300.
\[ \text{Experimental Probability of rolling a 6} = \frac{32}{300} \approx 0.1067 \]
Rounding this value gives approximately 0.107.
So the closest estimate of the experimental probability of rolling a 6 is:
0.107
Part B
The theoretical probability of rolling a 3 on a fair six-sided die is given by the ratio of favorable outcomes (rolling a 3) to total outcomes:
\[ \text{Theoretical Probability of rolling a 3} = \frac{1}{6} \]
To find the approximate relative frequency of rolling a 3 in 400 attempts, we multiply the theoretical probability by the number of trials:
\[ \text{Approximate Frequency of rolling a 3} = \text{Total Trials} \times \text{Theoretical Probability} = 400 \times \frac{1}{6} \approx 66.67 \]
Since the options are whole numbers, we can approximate to 64 (the closest option).
Thus, the value that represents an approximate relative frequency of rolling a 3 in 400 attempts is:
64