A bag has 5 red marbles, 4 green marbles and 3 blue marbles. All marbles are identical 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 marble?

Options

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

Answer

To find the probability of drawing a non-green marble from the bag, we can follow these steps:

### Step 1: Determine the total number of marbles in the bag.
- We have:
- 5 red marbles
- 4 green marbles
- 3 blue marbles

**Calculation:**
Total marbles = Number of red marbles + Number of green marbles + Number of blue marbles
Total marbles = 5 + 4 + 3 = 12

### Step 2: Determine the number of non-green marbles.
- Non-green marbles include red and blue marbles.
- We can find the number of non-green marbles by subtracting the number of green marbles from the total number of marbles.

**Calculation:**
Non-green marbles = Total marbles - Green marbles
Non-green marbles = 12 - 4 = 8

### Step 3: Calculate the probability of drawing a non-green marble.
- The probability (P) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

**Calculation:**
Probability of non-green marble = Number of non-green marbles / Total number of marbles
Probability of non-green marble = 8 / 12

### Step 4: Simplify the probability.
- We can simplify the fraction 8/12.

**Calculation:**
8/12 = 2/3

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

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