Question

A cube numbered from 1 to 6 will be rolled 400 times. The theoretical probability of rolling a 3 is 16
.

Select the value that represents an approximate relative frequency of rolling a 3 in 400 attempts.

(1 point)
Responses

24
24

64
64

200
200

240

Answer 1

The theoretical probability of rolling a 3 on a fair six-sided cube is \( \frac{1}{6} \).

To find the approximate relative frequency of rolling a 3 in 400 attempts, we can use the formula:

\[
\text{Expected number of times to roll a 3} = \text{Total rolls} \times \text{Probability of rolling a 3}
\]

Substituting the values:

\[
\text{Expected number of times to roll a 3} = 400 \times \frac{1}{6} \approx 66.67
\]

Since the options provided in your question are whole numbers, we can round this to the nearest whole number, which is 67.

None of the provided responses (24, 64, 200, 240) match this calculation. However, if we were to make a rough estimate and consider the closest option, the best match numerically would be "64."

The relative frequency of rolling a 3 in approximately 400 attempts could be closest to the response of **64**.