Susan rolled a number cube 20 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 4 3 3 3 2 5Fill in the table below. Round your answers to the nearest thousandth.(a) From Susan's results, compute the experimental probability of rolling a 5 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 5 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.
Question
Susan rolled a number cube 20 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 4 3 3 3 2 5Fill in the table below. Round your answers to the nearest thousandth.(a) From Susan's results, compute the experimental probability of rolling a 5 or 6.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 5 or 6.(c) Assuming that the cube is fair, choose the statement below that is true:With a large number of rolls, there must be no difference between the experimental and theoretical probabilities.With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.
Solution
(a) The experimental probability of rolling a 5 or 6 can be calculated by adding the number of times a 5 or 6 was rolled and dividing by the total number of rolls. In this case, Susan rolled a 5 or 6 a total of 7 times (2 times a 5 and 5 times a 6) out of 20 rolls. So, the experimental probability is 7/20 = 0.35.
(b) The theoretical probability of rolling a 5 or 6 on a fair six-sided cube is 2/6 = 0.333, because there are 2 favorable outcomes (rolling a 5 or 6) out of 6 possible outcomes.
(c) The correct statement is: "With a large number of rolls, there might be a difference between the experimental and theoretical probabilities, but the difference should be small." This is because, while the theoretical probability assumes a perfect, fair situation, the experimental probability is subject to random chance and variation, but should get closer to the theoretical probability as the number of trials increases.
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