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.
There are 6 sides so theoretical probability is 1/6
You measured 20/100 so experimental result was 1/5
To determine which statement about rolling a 3 is correct, we need to compare the theoretical probability and the experimental probability.
The theoretical probability of rolling a 3 on a fair number cube is calculated as the favorable outcomes (1) divided by the total possible outcomes (6). Therefore, the theoretical probability is 1/6.
The experimental probability is calculated by dividing the frequency of the specific outcome (in this case, the number 3) by the total number of trials. Given that the number 3 was rolled 20 times out of 100 trials, the experimental probability is 20/100, which simplifies to 1/5.
Comparing the two probabilities, we deduce that:
The theoretical probability is 1/6. The experimental probability is 1/5.
Therefore, the correct statement is: The theoretical probability is 1/6. The experimental probability is 1/5.
To determine the correct statement about rolling a 3, we need to compare the theoretical probability with the experimental probability.
The theoretical probability is the likelihood of an event happening based on mathematical principles. In this case, since we have a fair six-sided number cube, each face (including the number 3) has an equal chance of being rolled. Therefore, the theoretical probability of rolling a 3 on a fair six-sided die is 1/6.
The experimental probability is determined by conducting an actual experiment, in this case, rolling the number cube 100 times. To find the experimental probability of rolling a 3, we divide the frequency of the roll of the number 3 (which is 20) by the total number of rolls (which is 100). So, the experimental probability of rolling a 3 is 20/100, which simplifies to 1/5.
Comparing the two probabilities, we find that the correct statement is:
The theoretical probability is 1/6. The experimental probability is 1/5.