Answer :
To determine the approximate relative frequency of landing face-up on the cube, we can calculate the probability using the formula:
\[ \text{Probability} = \frac{\text{Number of times 3 is rolled}}{\text{Total number of rolls}} \]
Given that the cube is rolled 400 times:
\[ \text{Probability} = \frac{\text{Number of times 3 is rolled}}{400} \]
To find the probability of rolling a 3, we need to know how many times the number 3 appears on the cube. Since each face of the cube is numbered from 1 through 6, and the number 3 appears only once, the probability of rolling a 3 is:
\[ \text{Probability of rolling a 3} = \frac{1}{6} \]
Now, to find the approximate relative frequency, we multiply the probability of rolling a 3 by the total number of rolls:
\[ \text{Approximate relative frequency of rolling a 3} = \left( \frac{1}{6} \right) \times 400 \]
\[ \text{Approximate relative frequency of rolling a 3} = \frac{400}{6} \]
\[ \text{Approximate relative frequency of rolling a 3} \approx 66.67 \]
Therefore, two values that indicate an approximate relative frequency of rolling a 3 in 400 attempts are:
- 66.67 (rounded to the nearest hundredth)
- 67 (rounded to the nearest whole number)
