A bag has 6 yellow, 9 red, and 12 blue marbles. A marble is drawn at random. Find the probability that it is either red or blue.

Answer

To find the probability of drawing either a red or blue marble from a bag containing yellow, red, and blue marbles, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of each color of marbles:**
- Yellow marbles: 6
- Red marbles: 9
- Blue marbles: 12

2. **Calculate the total number of marbles:**
\[ \text{Total marbles} = \text{Yellow} + \text{Red} + \text{Blue} = 6 + 9 + 12 = 27 \]

3. **Determine the number of favorable outcomes (red or blue marbles):**
\[ \text{Favorable outcomes} = \text{Red} + \text{Blue} = 9 + 12 = 21 \]

4. **Use the probability formula:**
The probability \( P \) of an event is given by:
\[ P(\text{Red or Blue}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{21}{27} \]

5. **Simplify the fraction:**
To simplify \( \frac{21}{27} \), we can divide both the numerator and the denominator by their greatest common divisor, which is 3:
\[ \frac{21 \div 3}{27 \div 3} = \frac{7}{9} \]

6. **Conclusion:**
The probability of drawing either a red or blue marble is:
\[ \frac{7}{9} \]