What are the theoretical and experimental probabilities of rolling a 4 on a six-sided number cube? Write your answers as fractions in simplest form.

To find the theoretical probability of rolling a 4 on a six-sided number cube, we need to know the number of favorable outcomes and the total number of possible outcomes.

Favorable outcomes: There is only one way to roll a 4 on a six-sided number cube, which means there is one favorable outcome.

Total possible outcomes: Since a six-sided number cube has six faces, there are six possible outcomes (numbers 1 to 6).

Therefore, the theoretical probability of rolling a 4 is calculated by dividing the number of favorable outcomes by the total number of possible outcomes:

Theoretical probability = Number of favorable outcomes / Total number of possible outcomes
Theoretical probability = 1 / 6

Hence, the theoretical probability of rolling a 4 on a six-sided number cube is 1/6.

Now, let's consider experimental probability. To find the experimental probability, we need to actually perform the experiment (rolling the number cube) multiple times and record the results.

Assuming we roll the number cube 100 times and record the number of times we roll a 4, let's say we get 18 4s.

Experimental probability = Number of times the event occurs / Total number of trials
Experimental probability = 18 / 100

However, it is important to note that the experimental probability may vary based on the number of trials. The more trials performed, the more accurate the experimental probability will be.

Hence, the experimental probability of rolling a 4 on a six-sided number cube can be calculated as the fraction 18/100, but this may vary with more trials.

The theoretical probability of rolling a 4 on a six-sided number cube is determined by the total number of favorable outcomes divided by the total number of possible outcomes.

1. Favorable outcomes: There is only one face of the number cube with a 4.

2. Total possible outcomes: A standard six-sided number cube has six faces.

The theoretical probability of rolling a 4 is therefore 1/6.

The experimental probability of rolling a 4 can be found by conducting an experiment and recording the number of times a 4 is rolled out of a large number of trials.

For example, if you roll the number cube 100 times and you get a 4 20 times, then the experimental probability of rolling a 4 is 20/100, which simplifies to 1/5.