To find the probability of getting a number greater than 3 or an even number on a spinner numbered from 1 to 8, we can use the principle of inclusion-exclusion.
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Identify the outcomes: The possible outcomes of the spinner are: {1, 2, 3, 4, 5, 6, 7, 8}
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Numbers greater than 3: The numbers greater than 3 are: {4, 5, 6, 7, 8} This gives us 5 favorable outcomes.
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Even numbers: The even numbers are: {2, 4, 6, 8} This gives us 4 favorable outcomes.
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Numbers that are both greater than 3 and even: The even numbers greater than 3 are: {4, 6, 8} This gives us 3 favorable outcomes.
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Applying inclusion-exclusion: The total number of favorable outcomes for getting a number greater than 3 or an even number can be found using the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Where:
- \( P(A) \) is the number of outcomes greater than 3 (5 outcomes).
- \( P(B) \) is the number of even numbers (4 outcomes).
- \( P(A \cap B) \) is the number of outcomes that are both greater than 3 and even (3 outcomes).
Thus: \[ P(A \cup B) = 5 + 4 - 3 = 6 \]
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Total possible outcomes: There are 8 possible outcomes on the spinner.
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Calculating probability: The probability of getting a number greater than 3 or an even number is: \[ P(A \cup B) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{8} \]
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Reducing the fraction: The fraction \(\frac{6}{8}\) can be simplified: \[ \frac{6}{8} = \frac{3}{4} \]
Therefore, the final answer for the probability of getting a number greater than 3 or an even number is:
\[\frac{3}{4}\] or \(3\) fourths.