Question

a number cube is rolled 100 times as part of an experiment. 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:

To solve this, we analyze theoretical and experimental probability for rolling a 3 on a number cube:

Step 1: Theoretical Probability

A standard number cube has 6 faces (numbers 1–6). Only 1 face shows a 3.
Theoretical probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}$.

Step 2: Experimental Probability

Experimental probability depends on the results of the experiment (rolling the cube 100 times). However, the key here is recognizing that theoretical probability is fixed for a fair cube (1/6), while experimental probability is based on actual trials (and can vary, but the question asks which statement about the probability of rolling a 3 is correct).

Among the options, the correct one is:
"The theoretical probability is $\boldsymbol{\frac{1}{6}}$. The experimental probability is $\boldsymbol{\frac{1}{6}}$." (assuming the experiment’s results matched the theoretical probability, or the option with theoretical probability = 1/6 and consistent experimental logic).

(Note: If the options are labeled, e.g., Option A: "The theoretical probability is 1/6. The experimental probability is 1/6", then the answer is that option.)

Answer:

To solve this, we analyze theoretical and experimental probability for rolling a 3 on a number cube:

Step 1: Theoretical Probability

A standard number cube has 6 faces (numbers 1–6). Only 1 face shows a 3.
Theoretical probability = $\frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{1}{6}$.

Step 2: Experimental Probability

Experimental probability depends on the results of the experiment (rolling the cube 100 times). However, the key here is recognizing that theoretical probability is fixed for a fair cube (1/6), while experimental probability is based on actual trials (and can vary, but the question asks which statement about the probability of rolling a 3 is correct).

Among the options, the correct one is:
"The theoretical probability is $\boldsymbol{\frac{1}{6}}$. The experimental probability is $\boldsymbol{\frac{1}{6}}$." (assuming the experiment’s results matched the theoretical probability, or the option with theoretical probability = 1/6 and consistent experimental logic).

(Note: If the options are labeled, e.g., Option A: "The theoretical probability is 1/6. The experimental probability is 1/6", then the answer is that option.)