Question

In the table below are the results of rolling a number cube 400 times. Number 1 2 3 4 5 6 Frequency 35 211 32 41 38 43 A. Based on the observed frequencies, calculate the relative frequency for each number. B. Based on your results in A, do the outcomes for rolling the number cube appear to be equally likely? Explain your answer using complete sentences. C. If the outcomes do appear to be equally likely, why are the observed frequencies different for each number? If the outcomes do not appear to be equally likely, identify a possible reason for this result.

Answer 1

Relative frequencies are the ratio between the occurrence of the single outcome, and the total number of experiments. Since the die was rolled 400 times, we have

$\text{Relative frequency of number } i = \dfrac{\text{absolute frequency of } i}{400}$

So, we have

$\text{Relative frequency of } 1 = \dfrac{35}{400} = \dfrac{7}{80}$

$\text{Relative frequency of } 2 = \dfrac{211}{400}$

$\text{Relative frequency of } 3 = \dfrac{32}{400} = \dfrac{2}{25}$

$\text{Relative frequency of } 4 = \dfrac{41}{400}$

$\text{Relative frequency of } 5 = \dfrac{38}{400} = \dfrac{19}{200}$

$\text{Relative frequency of } 6 = \dfrac{43}{400}$

The outcomes do not appear to be equally likely, because 2 was rolled about 7 times as often as the others, whereas the occurrence should have been distributed in a more balanced way, i.e. every outcome should have had about 66 occurrences, i.e. about 400/6.

A possible reason could be an unfair die, modified so that it almost always returns the face with the 2

Answer 2

Answer:

A. The frequency of 35 would be 9%

The frequency of 211 would be 52%

The frequency of 32 would be 8%

The frequency of 41 would be 10%

The frequency of 38would be 10%

The frequency of 43 would be 11%

B. No because it is random.

C. According to the concept called the Law of Large Numbers, the more times you run the experiment, the more likely you would get the same outcome.

Step-by-step explanation: