A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that
it is blue ?

Answer

To find the probability that a marble drawn at random from the bag is blue, we can follow these steps:

### Step 1: Determine the total number of marbles in the bag.
- We have:
- 2 white marbles
- 4 blue marbles
- 6 red marbles

**Total number of marbles = Number of white marbles + Number of blue marbles + Number of red marbles**
\[ \text{Total} = 2 + 4 + 6 = 12 \]

### Step 2: Identify the number of favorable outcomes for drawing a blue marble.
- The number of blue marbles in the bag is 4.

### Step 3: Calculate the probability of drawing a blue marble.
- Probability is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes (blue marbles) is 4, and the total number of outcomes (total marbles) is 12.

\[ \text{Probability of blue marble} = \frac{4}{12} \]

### Step 4: Simplify the probability.
- We can simplify \(\frac{4}{12}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.

\[ \frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]

### Final Answer:
The probability that the marble drawn is blue is \(\frac{1}{3}\).

---