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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 assuming that the outcomes of her previous rolls will have an effect on the outcome of her next roll. A die roll is an independent event, meaning the outcome of one roll does not affect the outcome of another roll. Each time a standard number cube (a six-sided die) is rolled, the possible outcomes are always 1 through 6 regardless of previous rolls. Harriet should consider the proper sample space for the next roll to be {1, 2, 3, 4, 5, 6}. The fact that she has not rolled a 5 or 6 in her previous rolls does not change the sample space for her upcoming roll.
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