Question

alberto conducted an experiment by rolling a fair six - sided number cube 60 times. he rolled a 2 fifteen times. which statement about rolling a 2 in albertos experiment is correct?
the experimental probability of rolling a 2 is \\( \frac { 1 } { 4 } \\) and the theoretical probability of rolling a 2 is \\( \frac { 1 } { 6 } \\).
the experimental probability of rolling a 2 is \\( \frac { 1 } { 4 } \\) and the theoretical probability of rolling a 2 is \\( \frac { 1 } { 3 } \\).
the experimental probability of rolling a 2 is \\( \frac { 1 } { 6 } \\) and the theoretical probability of rolling a 2 is \\( \frac { 1 } { 4 } \\).
the experimental probability of rolling a 2 is \\( \frac { 1 } { 3 } \\) and the theoretical probability of rolling a 2 is \\( \frac { 1 } { 4 } \\).

Explanation:

Step1: Calculate theoretical probability

A fair six - sided cube has 6 possible outcomes (\(n = 6\)). The event of rolling a 2 is one favorable outcome (\(m=1\)). The formula for theoretical probability \(P=\frac{m}{n}\). So, the theoretical probability of rolling a 2 is \(\frac{1}{6}\).

Step2: Calculate experimental probability

Alberto rolled the cube \(N = 60\) times (total number of trials), and rolled a 2 \(M = 15\) times (number of successful trials). The formula for experimental probability \(P=\frac{M}{N}\). Substitute \(M = 15\) and \(N = 60\) into the formula: \(\frac{15}{60}=\frac{1}{4}\).

Answer:

The experimental probability of rolling a 2 is \(\frac{1}{4}\) and the theoretical probability of rolling a 2 is \(\frac{1}{6}\) (the second option).