To find \( P(6 \text{ or prime}) \), we need to identify the prime numbers in the set {5, 6, 7} and then determine how many of the total cards satisfy the condition of being either 6 or a prime number.
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Identify the prime numbers:
- 5 is prime
- 6 is not prime
- 7 is prime
The prime numbers in the set are 5 and 7.
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Identify the numbers that meet the condition:
- The event "6 or prime" includes:
- The number 6
- The prime numbers 5 and 7
Therefore, the numbers fulfilling our criteria are 5, 6, and 7.
- The event "6 or prime" includes:
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Count the favorable outcomes:
- The total count of favorable outcomes (5, 6, and 7) is 3.
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Count the total possible outcomes:
- The total number of cards is 3 (5, 6, 7).
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Calculate the probability: \[ P(6 \text{ or prime}) = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{3}{3} = 1 \]
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Convert to percentage: \[ P(6 \text{ or prime}) = 1 \times 100 = 100% \]
Therefore, \( P(6 \text{ or prime}) = 100% \).