Question

A six sided number cube labeled 1 through 6 is rolled 200 times. An even number is rolled 115 times. Compare the theoretical probability of rolling an even number with the relative frequency of rolling an even number and select one of the statements below that best describes the situation. Please provide an explanation and if it is A, B, C, or D.

Answer 1

The relative frequency can be calculated by making the division of the number of times the cube rolled an even number, and the amount of times the cube was rolled.

The relative frequency is

$\frac{115}{200}$

simplify the fraction

$\frac{23}{40}=0.575$

continue by finding the theorical probability which is found by the outcomes that are according to the statement and the total of possible outcomes

$\begin{gathered} \text{possible outcomes:}\mleft\lbrace1,2,3,4,5,6\mright\rbrace \\ \text{favorable outcomes:}\mleft\lbrace2,4,6\mright\rbrace \end{gathered}$

the theoretical probability is

$\frac{3}{6}=\frac{1}{2}=0.5$

According to this the theoretical probability is smaller than the relative frequency.