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Question: A standard number cube is rolled 5 times. The die lands on 1, 3, 2, 3, and 4. Harriet argues the sample space of the next roll is 1, 2, 3, and 4 because that has been the result of her previous rolls. Find Harriet’s error and correct it. Responses
Harriet's error is that she is assuming the outcomes of previous rolls affect the outcome of the next roll. In reality, the rolls of a standard number cube (a fair, six-sided die) are independent events, meaning that the outcome of one roll does not influence the outcome of the next roll. The correct sample space for the next roll should consist of all possible outcomes on a six-sided die, which are 1, 2, 3, 4, 5, and 6. Each roll has an equal probability of landing on any of these numbers, regardless of what the previous rolls were.
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