There are 5 red, 4 black and 3 blue balls in bag. A ball is drawn at random. Find the probability that the ball drawn is:
(i) black
(ii) red or black.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the total number of balls
We have:
- Red balls = 5
- Black balls = 4
- Blue balls = 3

Total number of balls = Red + Black + Blue

\[ \text{Total} = 5 + 4 + 3 = 12 \]

### Step 2: Find the probability of drawing a black ball
The number of black balls is 4. The probability \( P(B) \) of drawing a black ball is given by the formula:

\[ P(B) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{12} \]

Now, simplify the fraction:

\[ P(B) = \frac{4}{12} = \frac{1}{3} \]

### Step 3: Find the probability of drawing a red or black ball
To find the probability of drawing a red or black ball, we need to add the number of red balls and black balls:

Number of red balls = 5
Number of black balls = 4

Total number of favorable outcomes for red or black = Red + Black = 5 + 4 = 9

The probability \( P(R \cup B) \) of drawing a red or black ball is given by:

\[ P(R \cup B) = \frac{\text{Number of favorable outcomes for red or black}}{\text{Total number of outcomes}} = \frac{9}{12} \]

Now, simplify the fraction:

\[ P(R \cup B) = \frac{9}{12} = \frac{3}{4} \]

### Final Answers:
(i) The probability that the ball drawn is black: \( \frac{1}{3} \)

(ii) The probability that the ball drawn is red or black: \( \frac{3}{4} \)

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