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 1/6. the experimental probability is 1/6. the theoretical probability is 1/5. the experimental probability is 1/6. the theoretical probability is 1/6. the experimental probability is 1/5. the theoretical probability is 1/5. the experimental probability is 1/5.

Explanation:

Step1: Calculate Theoretical Probability

A fair number cube has 6 faces (numbers 1 - 6). The probability of rolling a 3 is the number of favorable outcomes (1, for rolling a 3) divided by total outcomes (6). So, theoretical probability \( P(\text{3})=\frac{1}{6} \).

Step2: Calculate Experimental Probability

Experimental probability is frequency of event divided by total trials. If the frequency of rolling a 3 is 20 (since \( \frac{20}{100}=\frac{1}{5} \), a common case with 100 rolls), then experimental probability \( P(\text{3})=\frac{\text{Frequency of 3}}{\text{Total rolls}}=\frac{20}{100}=\frac{1}{5} \).

Thus, the statement with theoretical \( \frac{1}{6} \) and experimental \( \frac{1}{5} \) is correct.

Answer:

The correct statement (assuming the frequency of rolling a 3 is 20, as it's a common setup with 100 rolls and 1/5 experimental probability: \( \frac{20}{100}=\frac{1}{5} \)) is: "The theoretical probability is \( \frac{1}{6} \). The experimental probability is \( \frac{1}{5} \)." (Corresponding to the option with these two probabilities, likely the third option in the list, e.g., if options are ordered as per the image, the one stating theoretical \( \frac{1}{6} \) and experimental \( \frac{1}{5} \)).