To find \( P(\text{blue or medium}) \), we need to use the formula for the probability of the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Where:
- \( A \) is the event of selecting a blue item,
- \( B \) is the event of selecting a medium item.
Step 1: Calculate \( P(A) \)
The total number of blue items is 6, as seen in the table. Therefore:
\[ P(\text{blue}) = \frac{6}{30} \]
Step 2: Calculate \( P(B) \)
To find the total number of medium items, we can add all medium items across colors (which is 7):
\[ P(\text{medium}) = \frac{7}{30} \]
Step 3: Calculate \( P(A \cap B) \)
Now we need to find the number of items that are both blue and medium. From the table, there is 1 blue medium item:
\[ P(\text{blue and medium}) = \frac{1}{30} \]
Step 4: Apply the formula
Now we can substitute these probabilities into our union formula:
\[ P(\text{blue or medium}) = P(\text{blue}) + P(\text{medium}) - P(\text{blue and medium}) \] \[ P(\text{blue or medium}) = \frac{6}{30} + \frac{7}{30} - \frac{1}{30} \] \[ P(\text{blue or medium}) = \frac{6 + 7 - 1}{30} = \frac{12}{30} \]
Thus,
\[ P(\text{blue or medium}) = \frac{12}{30} \]
So the correct response is:
\[ \frac{12}{30} \]
This corresponds to:
Response: \( \frac{12}{30} \)