A bag contains 8 red and 4 green balls . Find the probabilty that
the ball drawn is red when one ball is selected at random .

Options

A. `2/3`
B. `1/3`
C. `1/6`
D. `5/6`

Answer

To find the probability of drawing a red ball from a bag containing 8 red balls and 4 green balls, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the total number of balls**:
- The bag contains 8 red balls and 4 green balls.
- Total number of balls = Number of red balls + Number of green balls
\[ \text{Total number of balls} = 8 + 4 = 12 \]

2. **Identify the number of favorable outcomes**:
- The favorable outcome in this case is drawing a red ball.
- Number of favorable outcomes (red balls) = 8

3. **Use the probability formula**:
- The probability \( P \) of an event is given by the formula:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, \( E \) is the event of drawing a red ball.

4. **Substitute the values into the formula**:
\[ P(\text{Red ball}) = \frac{8}{12} \]

5. **Simplify the fraction**:
- To simplify \( \frac{8}{12} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4.
\[ P(\text{Red ball}) = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \]

6. **Conclusion**:
- The probability that the ball drawn is red is \( \frac{2}{3} \).