Question
PART B: A cube numbered from 1 through 6 is rolled 400 times. The probability of 3 landing face-up on the cube is
.
Select TWO values that indicate an approximate relative frequency of 3 landing face-up in 400 attempts.
A
24
B
64
C
70
D
200
E
240
Answers
GPT-4o mini
To determine the approximate relative frequency of the number 3 landing face-up when a cube is rolled 400 times, we first need to figure out the probability of rolling a 3 on a fair six-sided die.
The probability (P) of rolling a 3 on one roll is:
\[ P(3) = \frac{1}{6} \]
If the die is rolled 400 times, the expected number of times a 3 will land face-up can be calculated as follows:
\[ \text{Expected number of 3s} = P(3) \times \text{Number of rolls} \]
\[ = \frac{1}{6} \times 400 \]
\[ = \frac{400}{6} \approx 66.67 \]
Since we are looking for values that indicate an approximate relative frequency, we can round 66.67 to 70.
So the two values that indicate an approximate relative frequency of 3 landing face-up in 400 attempts are:
**B. 64** and **C. 70**.
The probability (P) of rolling a 3 on one roll is:
\[ P(3) = \frac{1}{6} \]
If the die is rolled 400 times, the expected number of times a 3 will land face-up can be calculated as follows:
\[ \text{Expected number of 3s} = P(3) \times \text{Number of rolls} \]
\[ = \frac{1}{6} \times 400 \]
\[ = \frac{400}{6} \approx 66.67 \]
Since we are looking for values that indicate an approximate relative frequency, we can round 66.67 to 70.
So the two values that indicate an approximate relative frequency of 3 landing face-up in 400 attempts are:
**B. 64** and **C. 70**.