Question

a six - sided, fair number cube is rolled 100 times as part of an experiment. the frequency of the roll of the number 3 is 20. which statement about rolling a 3 is correct?
the theoretical probability is \\( \frac { 1 } { 6 } \\). the experimental probability is \\( \frac { 1 } { 5 } \\).
the theoretical probability is \\( \frac { 1 } { 6 } \\). the experimental probability is \\( \frac { 1 } { 6 } \\).
the theoretical probability is \\( \frac { 1 } { 5 } \\). the experimental probability is \\( \frac { 1 } { 6 } \\).
the theoretical probability is \\( \frac { 1 } { 5 } \\). the experimental probability is \\( \frac { 1 } { 5 } \\).

Explanation:

Step1: Calculate theoretical probability

The theoretical probability of rolling a \(3\) on a fair six - sided cube is calculated as the number of favorable outcomes (getting a \(3\), which is \(1\) outcome) divided by the total number of possible outcomes (\(6\) outcomes: \(1,2,3,4,5,6\)). So, the theoretical probability \(P_{theoretical}=\frac{1}{6}\).

Step2: Calculate experimental probability

The experimental probability is calculated as the frequency of the event (rolling a \(3\), which is \(20\)) divided by the total number of trials (\(100\)). So, the experimental probability \(P_{experimental}=\frac{20}{100}=\frac{1}{5}\).

Answer:

The theoretical probability is \(\frac{1}{6}\) and the experimental probability is \(\frac{1}{5}\), so the correct statement is "The theoretical probability is \(\frac{1}{6}\). The experimental probability is \(\frac{1}{5}\)."