A bag contains 8 red, 7 orange and 9 green balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is :
(i) orange or green. (ii) not orange. (iii) neither green nor red.

Answer

To solve the problem, we will calculate the probabilities step by step for each of the three parts of the question.

### Given:
- Number of red balls = 8
- Number of orange balls = 7
- Number of green balls = 9

### Total number of balls:
Total = Number of red + Number of orange + Number of green
Total = 8 + 7 + 9 = 24

### (i) Probability of drawing an orange or green ball:
1. **Identify the favorable outcomes**:
- Number of orange balls = 7
- Number of green balls = 9
- Total favorable outcomes = 7 (orange) + 9 (green) = 16

2. **Calculate the probability**:
\[ P(\text{orange or green}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{16}{24} \]
- Simplifying \(\frac{16}{24}\):
\[ P(\text{orange or green}) = \frac{2}{3} \]

### (ii) Probability of not drawing an orange ball:
1. **Identify the favorable outcomes**:
- If we do not draw an orange ball, we can draw either a red or a green ball.
- Number of red balls = 8
- Number of green balls = 9
- Total favorable outcomes = 8 (red) + 9 (green) = 17

2. **Calculate the probability**:
\[ P(\text{not orange}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{17}{24} \]

### (iii) Probability of drawing neither a green nor a red ball:
1. **Identify the favorable outcomes**:
- If we do not draw a green or a red ball, we can only draw an orange ball.
- Number of orange balls = 7
- Total favorable outcomes = 7

2. **Calculate the probability**:
\[ P(\text{neither green nor red}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{7}{24} \]

### Summary of Results:
- (i) Probability of drawing an orange or green ball = \(\frac{2}{3}\)
- (ii) Probability of not drawing an orange ball = \(\frac{17}{24}\)
- (iii) Probability of drawing neither a green nor a red ball = \(\frac{7}{24}\)