Answered

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?

A. The theoretical probability is [tex]\(\frac{1}{6}\)[/tex]. The experimental probability is [tex]\(\frac{1}{6}\)[/tex].
B. The theoretical probability is [tex]\(\frac{1}{5}\)[/tex]. The experimental probability is [tex]\(\frac{1}{6}\)[/tex].
C. The theoretical probability is [tex]\(\frac{1}{6}\)[/tex]. The experimental probability is [tex]\(\frac{1}{5}\)[/tex].
D. The theoretical probability is [tex]\(\frac{1}{5}\)[/tex]. The experimental probability is [tex]\(\frac{1}{5}\)[/tex].



Answer :

GinnyAnswer
Let's analyze the problem step by step.

1. Theoretical Probability:
- A six-sided, fair number cube has equal probabilities for each face (number) to appear.
- The probability of rolling any particular number (e.g., 3) is the number of favorable outcomes (rolling a 3) divided by the total number of outcomes (6 faces).
- Therefore, the theoretical probability [tex]\( P(\text{rolling a 3}) \)[/tex] is [tex]\( \frac{1}{6} \)[/tex].

2. Experimental Probability:
- The experimental probability is calculated based on the observed data from an experiment.
- In this case, the number 3 appeared 20 times out of 100 rolls.
- The experimental probability [tex]\( P(\text{rolling a 3}) \)[/tex] is the frequency of rolling a 3 divided by the total number of rolls: [tex]\( \frac{20}{100} = \frac{1}{5} \)[/tex].

3. Comparing Probabilities:
- The theoretical probability, based on the fairness of the die, is [tex]\( \frac{1}{6} \)[/tex].
- The experimental probability, based on the results of this specific experiment, is [tex]\( \frac{1}{5} \)[/tex].

Given this information, the correct statement about rolling a 3 is:
- The theoretical probability is 1/6. The experimental probability is 1/5.

Therefore, the correct answer is the third option:
- The theoretical probability is 1/6. The experimental probability is 1/5.

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