a six - sided number cube is rolled 500 times. the results are 280 even numbers and 220 odd numbers. how…

a six - sided number cube is rolled 500 times. the results are 280 even numbers and 220 odd numbers. how does the relative frequency of rolling an even number compare to the theoretical probability? select from the drop - down menus to correctly complete the statements. the relative frequency of rolling an even number is choose... the theoretical probability. the theoretical probability is choose... and the relative frequency is choose...

a six - sided number cube is rolled 500 times. the results are 280 even numbers and 220 odd numbers. how does the relative frequency of rolling an even number compare to the theoretical probability? select from the drop - down menus to correctly complete the statements. the relative frequency of rolling an even number is choose... the theoretical probability. the theoretical probability is choose... and the relative frequency is choose...

Answer

Answer:

The relative frequency of rolling an even number is greater than the theoretical probability. The theoretical probability is $\frac{1}{2}$ and the relative frequency is $\frac{280}{500}=\frac{14}{25}$.

Explanation:

Step1: Calculate theoretical probability

On a six - sided die, there are 3 even numbers (2, 4, 6) out of 6 total numbers. So the theoretical probability $P=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate relative frequency

The relative frequency of rolling an even number is the number of times an even number is rolled divided by the total number of rolls. Given 280 even - number rolls out of 500 total rolls, so the relative frequency $f=\frac{280}{500}=\frac{14}{25}$.

Step3: Compare

We convert $\frac{1}{2}=\frac{25}{50}$ and $\frac{14}{25}=\frac{28}{50}$. Since $\frac{28}{50}>\frac{25}{50}$, the relative frequency is greater than the theoretical probability.