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

Answer

To solve the problem, we need to calculate the probabilities of drawing different colored balls from an urn containing 9 red, 7 white, and 4 black balls. Let's break this down step by step.

### Step 1: Calculate the Total Number of Balls
First, we need to find the total number of balls in the urn.

- Number of red balls = 9
- Number of white balls = 7
- Number of black balls = 4

**Total number of balls = 9 + 7 + 4 = 20**

### Step 2: Calculate the Probability of Drawing a Red Ball
The probability of drawing a red ball is given by the formula:

\[ P(\text{Red}) = \frac{\text{Number of Red Balls}}{\text{Total Number of Balls}} = \frac{9}{20} \]

### Step 3: Calculate the Probability of Drawing a White Ball
The probability of drawing a white ball is given by:

\[ P(\text{White}) = \frac{\text{Number of White Balls}}{\text{Total Number of Balls}} = \frac{7}{20} \]

### Step 4: Calculate the Probability of Drawing a Red or Black Ball
To find the probability of drawing either a red or a black ball, we add the probabilities of drawing a red ball and a black ball:

\[ P(\text{Red or Black}) = P(\text{Red}) + P(\text{Black}) = \frac{9}{20} + \frac{4}{20} = \frac{13}{20} \]

### Step 5: Calculate the Probability of Drawing a White or Black Ball
Similarly, to find the probability of drawing either a white or a black ball, we add the probabilities of drawing a white ball and a black ball:

\[ P(\text{White or Black}) = P(\text{White}) + P(\text{Black}) = \frac{7}{20} + \frac{4}{20} = \frac{11}{20} \]

### Step 6: Calculate the Probability of Not Drawing a Red Ball
The probability of not drawing a red ball can be calculated by subtracting the probability of drawing a red ball from 1:

\[ P(\text{Not Red}) = 1 - P(\text{Red}) = 1 - \frac{9}{20} = \frac{11}{20} \]

### Final Answers
1. Probability of drawing a red ball: **\(\frac{9}{20}\)**
2. Probability of drawing a white ball: **\(\frac{7}{20}\)**
3. Probability of drawing a red or black ball: **\(\frac{13}{20}\)**
4. Probability of drawing a white or black ball: **\(\frac{11}{20}\)**
5. Probability of not drawing a red ball: **\(\frac{11}{20}\)**