Amanda rolled a number cube 40 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 6 6 7 7 5 9Fill in the table below. Round your answers to the nearest thousandth.(a) From Amanda's results, compute the experimental probability of rolling a 4.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 4.(c) Assuming that the cube is fair, choose the statement below that is true: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 no difference between the experimental and theoretical probabilities.With a large number of rolls, there must be a large difference between the experimental and theoretical probabilities.
Question
Amanda rolled a number cube 40 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 6 6 7 7 5 9Fill in the table below. Round your answers to the nearest thousandth.(a) From Amanda's results, compute the experimental probability of rolling a 4.(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 4.(c) Assuming that the cube is fair, choose the statement below that is true: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 no difference between the experimental and theoretical probabilities.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 4 is calculated by dividing the number of times a 4 was rolled by the total number of rolls. In this case, Amanda rolled a 4, 7 times out of 40 rolls. So, the experimental probability is 7/40 = 0.175.
(b) The theoretical probability of rolling a 4 with a fair six-sided dice is 1/6, because there is one 4 on a dice with six faces. So, the theoretical probability is 1/6 = 0.167.
(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, in theory, the more times you roll the dice, the closer your experimental probability should get to the theoretical probability. However, there can still be some variation due to chance.
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