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 alberto’s 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 is the number of successful trials divided by the total number of trials. Alberto rolled a 2 fifteen times (assuming the "15" is the number of successes, as per the problem's context) and rolled the cube 60 times. So, experimental probability $= \frac{15}{60} = \frac{1}{4}$.

Step2: Calculate Theoretical Probability

A fair six - sided cube has 6 possible outcomes. The number of ways to roll a 2 is 1. So, theoretical probability $= \frac{1}{6}$.

Answer:

The option where 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 from the top, assuming the options are ordered as presented: "The experimental probability of rolling a 2 is $\frac{1}{4}$ and the theoretical probability of rolling a 2 is $\frac{1}{6}$").