Lisa rolled a number cube 25 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 5 2 6 4 7 1Answer the following. Round your answers to the nearest thousandths.(a)From Lisa's results, compute the experimental probability of rolling an odd number.(b)Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.(c)Assuming that the cube is fair, choose the statement below that is true.
Question
Lisa rolled a number cube 25 times and got the following results.Outcome Rolled 1 2 3 4 5 6Number of Rolls 5 2 6 4 7 1Answer the following. Round your answers to the nearest thousandths.(a)From Lisa's results, compute the experimental probability of rolling an odd number.(b)Assuming that the cube is fair, compute the theoretical probability of rolling an odd number.(c)Assuming that the cube is fair, choose the statement below that is true.
Solution
(a) The experimental probability of rolling an odd number can be calculated by dividing the total number of successful outcomes (rolling an odd number) by the total number of trials. The odd numbers on a dice are 1, 3, and 5. From Lisa's results, she rolled an odd number (1, 3, or 5) a total of 5 (for 1) + 6 (for 3) + 7 (for 5) = 18 times. She rolled the dice 25 times in total. So, the experimental probability of rolling an odd number is 18/25 = 0.72 or 72%.
(b) The theoretical probability of rolling an odd number on a fair dice can be calculated by dividing the total number of successful outcomes (rolling an odd number) by the total number of possible outcomes. A dice has 6 faces, and half of them (3 faces: 1, 3, and 5) are odd. So, the theoretical probability of rolling an odd number is 3/6 = 0.5 or 50%.
(c) Assuming that the cube is fair, the statement that is true is: "The theoretical probability of an event is the same as the experimental probability as the number of trials increases." This is based on the law of large numbers, which states that as the number of trials increases, the experimental probability will get closer to the theoretical probability. In this case, Lisa's experimental probability (72%) is higher than the theoretical probability (50%), which could be due to the relatively small number of trials (25 rolls). If she were to continue rolling the dice many more times, we would expect her experimental probability to get closer to 50%.
Similar Questions
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