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 $\frac{1}{3}$ and the theoretical probability of rolling a 2 is $\frac{1}{4}$.

• 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 $\frac{1}{4}$ and the theoretical probability of rolling a 2 is $\frac{1}{6}$.

• the experimental probability of rolling a 2 is $\frac{1}{6}$ and the theoretical probability of rolling a 2 is $\frac{1}{4}$.

Explanation:

Step1: Calculate experimental probability

Experimental probability = $\frac{\text{Number of times 2 is rolled}}{\text{Total number of rolls}}$ = $\frac{15}{60}$ = $\frac{1}{4}$.

Step2: Calculate theoretical probability

A fair six - sided cube has 6 faces. The probability of rolling a 2 (theoretical) = $\frac{\text{Number of favorable outcomes (rolling a 2)}}{\text{Total number of possible outcomes}}$ = $\frac{1}{6}$.

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 third option).