To determine if Caitlyn made an error in calculating the probability of the complement of rolling a number greater than 2 on a 6-sided number cube, let's analyze the situation step by step.
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Understanding the event: The event "rolling a number greater than 2" means rolling either a 3, 4, 5, or 6. Therefore, there are 4 favorable outcomes for this event.
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Complement of the event: The complement of rolling a number greater than 2 is rolling a number less than or equal to 2. The possible outcomes for this complement event on a 6-sided die are 1 and 2. Thus, there are 2 favorable outcomes for this complement event.
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Calculating probabilities:
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The total number of outcomes when rolling a die is 6 (the numbers 1 through 6).
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The probability of rolling a number greater than 2 (3, 4, 5, or 6) is calculated as: \[ P(> 2) = \frac{\text{number of favorable outcomes (> 2)}}{\text{total outcomes}} = \frac{4}{6} = \frac{2}{3} \]
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The probability of the complement event (rolling a number less than or equal to 2) is: \[ P(\leq 2) = \frac{\text{number of favorable outcomes (≤ 2)}}{\text{total outcomes}} = \frac{2}{6} = \frac{1}{3} \]
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Verifying the complement: The probabilities of an event and its complement must sum to 1: \[ P(> 2) + P(\leq 2) = \frac{2}{3} + \frac{1}{3} = \frac{3}{3} = 1 \]
Since Caitlyn calculated \(P(\leq 2)\) correctly as \(\frac{1}{3}\), she did not make an error in that calculation.
However, it's important to clarify her approach. If she calculated \(P(\leq 2)\) as part of finding the probability of the complement, that part is correct. But if her intention or the question was misrepresented or misunderstood, we might need more context. As it stands, based on the information provided, Caitlyn did not make an error in calculating the probability of the complement of rolling a number greater than 2.