In a bag, there are 2 rad balls, 3 green balls and 4 brown balls. Find the probability of drawing a ball at random being red or green.

Options

A. `(5)/(9)`
B. `(1)/(4)`
C. `(1)/(5)`
D. `(4)/(9)`

Explanation

To find the probability of drawing a ball at random that is either red or green from a bag containing different colored balls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of each color of balls:**
- Red balls = 2
- Green balls = 3
- Brown balls = 4

2. **Calculate the total number of balls in the bag:**
\[ \text{Total balls} = \text{Red balls} + \text{Green balls} + \text{Brown balls} \]
\[ \text{Total balls} = 2 + 3 + 4 = 9 \]

3. **Determine the number of favorable outcomes (red or green balls):**
- Favorable outcomes (Red or Green) = Red balls + Green balls
\[ \text{Favorable outcomes} = 2 + 3 = 5 \]

4. **Use the probability formula:**
The probability \( P \) of an event is given by:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Here, the event is drawing a red or green ball.
\[ P(\text{Red or Green}) = \frac{\text{Favorable outcomes}}{\text{Total balls}} = \frac{5}{9} \]

5. **Conclusion:**
The probability of drawing a ball that is either red or green is \( \frac{5}{9} \).