What is the theoretical probability of rolling an 8, and how do the experimental and theoretical probabilities compare?
Responses
A The theoretical probability is 19.4%. The experiment rolled less 8's than would be expected theoretically.The theoretical probability is 19.4%. The experiment rolled less 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 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.
Well, since you're asking a theoretical question, let me give you a theoretical answer: the theoretical probability of rolling an 8 is 16.7%. However, if we're talking about the experimental probability, it seems like the experiment rolled less 8's than would be expected theoretically. So, in conclusion, the theoretical and experimental probabilities don't quite align. Maybe the dice just have something against the number 8!
The correct answer is B. The theoretical probability of rolling an 8 is 16.7%. The experiment rolled less 8's than would be expected theoretically.
The correct answer is B. The theoretical probability of rolling an 8 can be calculated by dividing the number of favorable outcomes (in this case, the number of possible combinations that result in an 8) by the number of total outcomes (which is the number of possible combinations when rolling two dice).
In this case, when rolling two dice, there are 36 possible outcomes (6 sides on the first die multiplied by 6 sides on the second die). Out of these 36 outcomes, there are 5 combinations that result in an 8: (2,6), (3,5), (4,4), (5,3), and (6,2).
Therefore, the theoretical probability of rolling an 8 is 5/36, which is approximately 0.138 or 13.9%.
To compare the experimental and theoretical probabilities, the experimenter would need to conduct a number of trials where two dice are rolled, and then count the number of times an 8 is rolled. The experimental probability of rolling an 8 would be determined by dividing the number of successful outcomes (number of times an 8 is rolled) by the total number of trials conducted.
If the experiment rolled less 8's than would be expected theoretically, it means that the experimental probability is lower than the theoretical probability, indicating that the outcome is less likely to occur than predicted by the theory.
Therefore, the correct statement is: The theoretical probability is 16.7%. The experiment rolled less 8's than would be expected theoretically.