Question

Use the table to answer the question.

Size
Color Large Medium Small TOTAL
Yellow 2 4 11 17
Blue 1 1 4 6
Red 1 2 4 7
TOTAL 4 7 19 30
What is P(blue or medium)
?

(1 point)
Responses

1030
Start Fraction 10 over 30 End Fraction

1230
Start Fraction 12 over 30 End Fraction

1330
Start Fraction 13 over 30 End Fraction

630

Answer 1

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: \( \frac{12}{30} \)**