位置4的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13122356清除选择

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BlackTom AI · Accepted Answer

以下为题干与选项的逐步分析，帮助理解各选项的合理性与不合理之处。
题干要点：抛掷一个公平的六面骰子，X 表示点数，取值为1到6。要求计算 P(2 ≤ X ≤ 5)，即点数在2、3、4、5之间的概率。
选项分析：
选项1: 1
3
这表示分数为 1/3。若要判断其是否合适，需要看分子分母是否对应事件的可能结果数与样本空间规模。事件中包含的点数有 2、3、4、5，共4种可能性；样本空间共有6种可能性。因此正确的分数应是 4/6，化简为 2/3，而非 1/3。
选项2: 1
2
这表示分数为 1/2。1/2 对应的事件应包含3种或更多的等概率结果，但在本题中事件包含4种结果（2、3、4、5），与样本空间的6项相比，1/2 相当于 3/6，少了 1/6 的可能性，因此这个选项低估了事件的概率。
选项3: 2
3
这表示分数为 2/3。此时分子是2、分母是3，若将分式还原为与样本空间相关的形式，相当于 4/6 的简化结果，因包含的点数为 2、3、4、5 共4种，6种总样本空间，因此 4/6 = 2/3，与题意完全一致，这个选项在数值上与实际概率相符。
选项4: 5
6
这表示分数为 5/6。5/6 体现出事件几乎覆盖整个样本空间，但本题事件只覆盖4/6 的概率，因此 5/6 与实际情况不符，属于高估。
综合来看，最接近实际计算的判断是：事件包含4种可能结果（2、3、4、5），样本空间有6种可能，因此 P(2 ≤ X ≤ 5) = 4/6 = 2/3，与 2
3 相符。
备注：若需要直观核对，可以直接列出符合条件的点数：{2, 3, 4, 5}，共4种，对应样本空间6种，总概率为 4/6 = 2/3。

位置4的问题 Suppose X is a random variable representing rolling a six-sided dice. Assume the dice is fair, so there is an equal probability of rolling any number 1 through 6. What is the following probability? P(2≤X≤5) 13122356清除选择

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