Maria rolled a number cube 25 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 8 8 2 3 4 0Fill in the table below. Round your answers to the nearest thousandth.(a) From Maria's results, compute the experimental probability of rolling a 3 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 3 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.The experimental and theoretical probabilities must always be equal.
Question
Maria rolled a number cube 25 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 8 8 2 3 4 0Fill in the table below. Round your answers to the nearest thousandth.(a) From Maria's results, compute the experimental probability of rolling a 3 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 3 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.The experimental and theoretical probabilities must always be equal.
Solution
(a) The experimental probability of rolling a 3 or 6 is calculated by dividing the number of times a 3 or 6 was rolled by the total number of rolls. In this case, Maria rolled a 3 twice and a 6 zero times, for a total of 2 times. She rolled the cube 25 times in total. So, the experimental probability is 2/25 = 0.08.
(b) The theoretical probability of rolling a 3 or 6 on a fair cube is calculated by dividing the number of favorable outcomes (rolling a 3 or 6) by the total number of possible outcomes (6, because a cube has 6 faces). There are 2 favorable outcomes (3 and 6), so the theoretical probability is 2/6 = 0.333.
(c) The correct statement is: As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is because, in theory, the more times you roll the cube, the closer your results should get to the expected probabilities. However, because each roll is independent (the result of one roll doesn't affect the results of any other rolls), the experimental and theoretical probabilities might not be exactly equal, even after a large number of rolls.
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