位置1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) 13231256清除选择

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The problem states a fair six-sided die with equally likely outcomes 1 through 6, and asks for P(2 ≤ X ≤ 5).
Option 1: 1/3. This would correspond to 2 out of 6 outcomes or 4 out of 12, which is not accurate for the range 2 to 5 (that range includes 4 outcomes: 2, 3, 4, 5). So 1/3 is too small.
Option 2: 2/3. The interval 2 ≤ X ≤ 5 includes the values 2, 3, 4, and 5 — four favorable outcomes. With a fair die, each outcome has probability 1/6, so P = 4 × (1/6) = 4/6 = 2/3. This matches the correct probability.
Option 3: 1/2. That would correspond to 3 favorable outcomes out of 6, which would be if only three numbers were included in the interval. But the interval 2 to 5 includes four numbers, not three, so 1/2 is incorrect.
Option 4: 5/6. This would imply almost all outcomes are favorable, leaving only one outcome unfavorable. However, within 2 to 5 there are four favorable outcomes and two unfavorable (1 and 6), so 5/6 overestimates the probability.
In summary, the correct counting shows four favorable outcomes (2, 3, 4, 5) out of six possible outcomes, giving 4/6 = 2/3. The other options miscount the favorable set or overlook the uniform probability across all six outcomes.

位置1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) 13231256清除选择

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