What is the theoretical probability of rolling an 8, and how do the experimental and theoretical probabilities compare?
Responses
A The theoretical probability is 11.1%. The experiment rolled more 8's than would be expected theoretically.The theoretical probability is 11.1%. The experiment rolled more 8's than would be expected theoretically.
B The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.
C The theoretical probability is 13.9%. The experiment rolled more 8's than would be expected theoretically.The theoretical probability is 13.9%. The experiment rolled more 8's than would be expected theoretically.
D The theoretical probability is 19.4%. The experiment rolled less 8's than would be expected theoretically.
A The theoretical probability is 11.1%. The experiment rolled more 8's than would be expected theoretically.
To find the theoretical probability of rolling an 8, we need to know the number of favorable outcomes (rolling an 8) and the total number of possible outcomes. If we assume that the total number of outcomes is 6 (since a standard die has 6 sides), then the number of favorable outcomes (rolling an 8) is 0 since an 8 is not a possible outcome on a standard die. Therefore, the theoretical probability of rolling an 8 is 0%.
Now, if the experimental probability of rolling an 8 is different from the theoretical probability, it means that the experiment yielded different results than what would be expected based on the theoretical probability.
Based on the given options, the correct answer would be:
B. The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.
The correct answer is D.
The theoretical probability of rolling an 8 can be calculated by dividing the number of favorable outcomes (getting an 8) by the number of possible outcomes (the total number of outcomes when rolling a fair six-sided die).
In this case, the favorable outcome is rolling an 8, and there is only one way to roll an 8 (when the die shows the number 8). The total number of possible outcomes when rolling a fair six-sided die is 6 (since there are six sides numbered 1 to 6). Therefore, the theoretical probability of rolling an 8 is 1/6, which is approximately 16.7%.
The experimental probability, on the other hand, is determined by conducting an actual experiment and counting the number of times an 8 is rolled over a large number of trials. The experimental and theoretical probabilities may not always be equal due to random variations.
From the given options, option D states that the experiment rolled less 8's than would be expected theoretically, which means the experimental probability is less than the theoretical probability.