Question

Part A

A cube numbered from 1 to 6 is rolled 300 times. The number 6 is rolled 32 times.

Which value is the closest estimate of the experimental probability of rolling a 6?

(1 point)
Responses

0.087

0.107

0.127

0.188
Question 2
Part B

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

64

200

240

Answer 1

### 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**