Question

Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.

Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome

Outcome: 1 2 3 4
Relative Frequency : 0.23 0.24 0.26 0.27

Which statements about Dina's experiment are true?

Select EACH correct answer.

A) The relative frequencies in the table are reasonably close.
B) The theoretical probability of rolling an even number is 0.51.
C) The relative frequency of rolling an even number is 0.51.
D) The number cube is not likely to be fair.

Answer 1

Option A and C are true.

Explanation:

Given : Dina has a number cube that she uses for a game. The number cube has the shape of a triangular pyramid, with 4 faces numbered 1 through 4.

Dina rolls the number cube 100 times and records the results. She calculates the relative frequency of each outcome

Outcome : 1 2 3 4

Relative Frequency : 0.23 0.24 0.26 0.27

To find : Which statements about Dina's experiment are true?

Solution :

Option A - The relative frequencies in the table are reasonably close.

This statement is true, as we see that the relative frequency are all between 0.23 to 0.27 that are reasonably close.

Option B - The theoretical probability of rolling an even number is 0.51.

This statement is not true, as the theoretical probability of rolling even numbers is

2 even numbers from 4, so probability is

`P=(2)/(4)=(1)/(2)=0.5`

Option C - The relative probability of rolling an even number is 0.51.

This statement is true, as the relative frequency of an even number is 0.24+0.27=0.51

Option D - The number cube is not likely to be fair.

The statement is not true, as the relative frequency are reasonably close which implies that the number cube is likely to be fair and sum of the relative frequency is 1.

Therefore, Option A and C are correct.

Answer 2

A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.

Explanation:

The relative frequencies given are at most 0.02 apart. This means they are reasonably close.

The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.

However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.

Since the relative frequencies are reasonably close, the number cube is likely to be fair.