An urn contains 9 red, 7 white and 4 black balls. A ball is drawn at random. Find the probability that the ball drawn is
(i) red (ii) white (iii) red or white
(iv) white or black (v) not white

Answer

To solve the problem, we will calculate the probability for each part step by step.

### Given:
- Red balls = 9
- White balls = 7
- Black balls = 4

### Total number of balls:
Total = Red + White + Black = 9 + 7 + 4 = 20

### (i) Probability of drawing a red ball:
The probability of an event is given by the formula:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

For a red ball:
- Number of favorable outcomes = 9 (red balls)
- Total outcomes = 20

So,
\[ P(\text{Red}) = \frac{9}{20} \]

### (ii) Probability of drawing a white ball:
For a white ball:
- Number of favorable outcomes = 7 (white balls)
- Total outcomes = 20

So,
\[ P(\text{White}) = \frac{7}{20} \]

### (iii) Probability of drawing a red or white ball:
The probability of drawing a red or white ball can be calculated by adding the probabilities of drawing a red ball and a white ball:
\[ P(\text{Red or White}) = P(\text{Red}) + P(\text{White}) \]

So,
\[ P(\text{Red or White}) = \frac{9}{20} + \frac{7}{20} = \frac{16}{20} = \frac{4}{5} \]

### (iv) Probability of drawing a white or black ball:
Similarly, we can calculate the probability of drawing a white or black ball:
\[ P(\text{White or Black}) = P(\text{White}) + P(\text{Black}) \]

For a black ball:
- Number of favorable outcomes = 4 (black balls)
- Total outcomes = 20

So,
\[ P(\text{Black}) = \frac{4}{20} = \frac{1}{5} \]

Now, adding the probabilities:
\[ P(\text{White or Black}) = \frac{7}{20} + \frac{4}{20} = \frac{11}{20} \]

### (v) Probability of not drawing a white ball:
The probability of not drawing a white ball can be found by subtracting the probability of drawing a white ball from 1:
\[ P(\text{Not White}) = 1 - P(\text{White}) \]

So,
\[ P(\text{Not White}) = 1 - \frac{7}{20} = \frac{20 - 7}{20} = \frac{13}{20} \]

### Summary of Results:
1. Probability of red ball = \( \frac{9}{20} \)
2. Probability of white ball = \( \frac{7}{20} \)
3. Probability of red or white ball = \( \frac{4}{5} \)
4. Probability of white or black ball = \( \frac{11}{20} \)
5. Probability of not white ball = \( \frac{13}{20} \)