A bag has 5 red marbles, 4 green marbles and 3 blue marbles. All marbles are indentical in all respects other than colour. A marble is taken out from the bag without looking into it. What is the probability that it is a non-green marbles?

Options

A. `(1)/(3)`
B. `(2)/(3)`
C. `(7)/(12)`
D. `(5)/(12)`

Answer

To solve the problem of finding the probability of drawing a non-green marble from a bag containing red, green, and blue marbles, we can follow these steps:

### Step 1: Identify the total number of marbles in the bag.
- The bag contains:
- Red marbles: 5
- Green marbles: 4
- Blue marbles: 3

**Total marbles = Red + Green + Blue = 5 + 4 + 3 = 12**

### Step 2: Determine the number of non-green marbles.
- Non-green marbles are either red or blue.
- The number of non-green marbles is:
- Red marbles: 5
- Blue marbles: 3

**Total non-green marbles = Red + Blue = 5 + 3 = 8**

### Step 3: Calculate the probability of drawing a non-green marble.
- Probability is calculated as the number of favorable outcomes divided by the total number of outcomes.

**Probability of non-green marble = (Number of non-green marbles) / (Total number of marbles)**

**Probability = 8 / 12**

### Step 4: Simplify the probability.
- Simplifying \( \frac{8}{12} \):
- Both the numerator and denominator can be divided by 4.

**Probability = \( \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \)**

### Conclusion:
The probability that a marble drawn from the bag is a non-green marble is \( \frac{2}{3} \).

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