To find \( P(\text{blue or medium}) \), we need to use the principle of inclusion-exclusion. This means we will find the probability of selecting a blue item, the probability of selecting a medium item, and then subtract the probability of selecting an item that is both blue and medium (to avoid double counting).
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Count the total number of items: The total is 30.
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Count the number of blue items: From the table:
- Total blue items = \( 6 \)
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Count the number of medium items: From the table:
- Total medium items = \( 7 \)
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Count the number of items that are both blue and medium: From the table:
- Blue medium items = \( 1 \)
Now, we can apply the formula: \[ P(\text{blue or medium}) = P(\text{blue}) + P(\text{medium}) - P(\text{blue and medium}) \]
Calculating each probability:
- \( P(\text{blue}) = \frac{6}{30} \)
- \( P(\text{medium}) = \frac{7}{30} \)
- \( P(\text{blue and medium}) = \frac{1}{30} \)
Now substituting these values into the inclusion-exclusion formula: \[ P(\text{blue or medium}) = \frac{6}{30} + \frac{7}{30} - \frac{1}{30} = \frac{6 + 7 - 1}{30} = \frac{12}{30} \]
Simplifying \( \frac{12}{30} \): \[ \frac{12}{30} = \frac{2}{5} \]
Thus, the probability of selecting either a blue item or a medium item is \( \frac{12}{30} \).
The correct answer is: Start Fraction 12 over 30 End Fraction.