A bag contains 8 red and 4_ green balls. One ball is selected at random. Find the probability that the ball drawn is red.

Options

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

Answer

To solve the problem of finding the probability that a ball drawn from a bag containing 8 red balls and 4 green balls is red, 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
- Total number of balls = 8 + 4 = 12

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

3. **Calculate the Probability:**
- The probability of an event is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
- Here, the event is drawing a red ball.
- Therefore, the probability of drawing a red ball is:
\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} = \frac{8}{12} \]

4. **Simplify the Fraction:**
- We can simplify \(\frac{8}{12}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4.
- So, \(\frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)

5. **Final Answer:**
- The probability that the ball drawn is red is:
\[ P(\text{Red}) = \frac{2}{3} \]

### Summary:
The probability of drawing a red ball from the bag is \(\frac{2}{3}\).

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