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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

630
Start Fraction 6 over 30 End Fraction

1330

1 answer

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

\[ P(\text{blue or medium}) = P(\text{blue}) + P(\text{medium}) - P(\text{blue and medium}) \]

Now, let's calculate each of these probabilities from the table:

  1. Calculate \( P(\text{blue}) \):

    • Total number of blue items = 6 (from the TOTAL column for Blue)
    • Total number of items = 30
    • So, \( P(\text{blue}) = \frac{6}{30} \)

  2. Calculate \( P(\text{medium}) \):

    • Total number of medium items = 7 (from the TOTAL column for Medium)
    • So, \( P(\text{medium}) = \frac{7}{30} \)

  3. Calculate \( P(\text{blue and medium}) \):

    • Blue and medium = 1 (from the cell in the table corresponding to Blue and Medium)
    • So, \( P(\text{blue and medium}) = \frac{1}{30} \)

Now, we can combine these results:

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

Thus, \( P(\text{blue or medium}) = \frac{12}{30} \).

The correct response is \( \frac{12}{30} \).