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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

630
Start Fraction 6 over 30 End Fraction

1030
Start Fraction 10 over 30 End Fraction

1230
Start Fraction 12 over 30 End Fraction

1330
Start Fraction 13 over 30 End Fraction

1 answer

To find \( P(\text{blue or medium}) \), we can use the principle of inclusion-exclusion. This probability can be calculated as follows:

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

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

    • The total number of blue items is 6.
    • Therefore, \( P(\text{blue}) = \frac{6}{30} \).

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

    • The total number of medium items is 7.
    • Therefore, \( P(\text{medium}) = \frac{7}{30} \).

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

    • The number of blue items that are medium is 1.
    • Therefore, \( P(\text{blue and medium}) = \frac{1}{30} \).

Now, substituting these values into the inclusion-exclusion 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, the simplified answer is:

\[ P(\text{blue or medium}) = \frac{12}{30} \]

So the answer is:

\( \frac{12}{30} \) (or 1230 in your response options).