Use the table to answer the question.

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)

10/30
12/30
13/30
6/30

Answer 1

To find \( P(\text{Blue or Medium}) \), we can use the principle of inclusion-exclusion:

\[ P(\text{Blue or Medium}) = P(\text{Blue}) + P(\text{Medium}) - P(\text{Blue and Medium}) \]

1. Calculate \( P(\text{Blue}) \):
   There are 6 blue items out of 30 total items:

   \[ P(\text{Blue}) = \frac{6}{30} \]

2. Calculate \( P(\text{Medium}) \):
   We need to find the total number of medium-sized items. The table shows:

   • Medium Yellow: 4
   • Medium Blue: 1
   • Medium Red: 2

   Total Medium = 4 + 1 + 2 = 7

   So,

   \[ P(\text{Medium}) = \frac{7}{30} \]

3. Calculate \( P(\text{Blue and Medium}) \):
   From the table, there is 1 blue medium item.

   \[ P(\text{Blue and Medium}) = \frac{1}{30} \]

4. Now substitute into the formula:

   \[ P(\text{Blue or Medium}) = P(\text{Blue}) + P(\text{Medium}) - P(\text{Blue and Medium}) \]

   \[ P(\text{Blue or Medium}) = \frac{6}{30} + \frac{7}{30} - \frac{1}{30} = \frac{6 + 7 - 1}{30} = \frac{12}{30} \]

So, the answer is:

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

Thus, the correct option is:

12/30