Question

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 1330 Start Fraction 13 over 30 End Fraction 1230 Start Fraction 12 over 30 End Fraction 1030 Start Fraction 10 over 30 End Fraction 630 Start Fraction 6 over 30 End Fraction Skip to navigation

Answer 1

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

First, we need to find the probabilities of events \( A \) (being blue) and \( B \) (being medium).

1. **Find \( P(\text{blue}) \)**:
- Total blue items = 6
- Thus, \( P(\text{blue}) = \frac{6}{30} = \frac{1}{5} \).

2. **Find \( P(\text{medium}) \)**:
- Total medium items = 7
- Thus, \( P(\text{medium}) = \frac{7}{30} \).

3. **Find \( P(\text{blue and medium}) \)**:
- Blue and medium items = 1 (from the table).
- Thus, \( P(\text{blue and medium}) = \frac{1}{30} \).

Now we can apply the inclusion-exclusion principle:

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

Now we simplify \( \frac{12}{30} \):

\[
\frac{12}{30} = \frac{2}{5}
\]

Thus, the final result is

\[
\frac{12}{30} \text{ or } \frac{2}{5}
\]

Based on the given options, the answer is:

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