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The probability of an event is greater t...

The probability of an event is greater than 1.

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To determine whether the statement "The probability of an event is greater than 1" is true or false, we can analyze the concept of probability step by step. ### Step-by-Step Solution: 1. **Understanding Probability**: The probability of an event \( E \) is defined as: \[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] 2. **Analyzing the Statement**: The statement claims that the probability of an event is greater than 1. Mathematically, this can be expressed as: \[ P(E) > 1 \] 3. **Interpreting the Inequality**: If we assume that \( P(E) > 1 \), this implies: \[ \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} > 1 \] This can be rearranged to: \[ \text{Number of favorable outcomes} > \text{Total number of outcomes} \] 4. **Logical Conclusion**: The total number of outcomes represents all possible outcomes of an event. It is impossible for the number of favorable outcomes to exceed the total number of outcomes. For instance, if there are 5 balls in a bag, you cannot have more than 5 favorable outcomes (e.g., red balls) if you are only selecting from those 5 balls. 5. **Final Conclusion**: Since it is logically impossible for the number of favorable outcomes to be greater than the total number of outcomes, the statement "The probability of an event is greater than 1" is **false**. ### Final Answer: The statement is **false**. ---
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