A bag contains 6 red, 5 black and 4 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is :
(i) white (ii) red (iii) not black (iv) red or white.

Answer

To solve the problem step by step, we will calculate the probabilities for each of the scenarios given.

### Step 1: Determine the total number of balls.
- We have:
- Red balls = 6
- Black balls = 5
- White balls = 4

**Total number of balls = Red + Black + White = 6 + 5 + 4 = 15**

### Step 2: Calculate the probability of drawing a white ball.
- The number of favorable outcomes for drawing a white ball = 4 (since there are 4 white balls).
- The total number of outcomes = 15 (total balls).

**Probability of drawing a white ball = (Number of favorable outcomes) / (Total outcomes) = 4 / 15**

### Step 3: Calculate the probability of drawing a red ball.
- The number of favorable outcomes for drawing a red ball = 6 (since there are 6 red balls).
- The total number of outcomes = 15 (total balls).

**Probability of drawing a red ball = (Number of favorable outcomes) / (Total outcomes) = 6 / 15 = 2 / 5 (after simplification)**

### Step 4: Calculate the probability of drawing a ball that is not black.
- The number of black balls = 5.
- The number of balls that are not black = Total balls - Black balls = 15 - 5 = 10.

**Probability of drawing a ball that is not black = (Number of favorable outcomes) / (Total outcomes) = 10 / 15 = 2 / 3 (after simplification)**

### Step 5: Calculate the probability of drawing a red or white ball.
- The number of favorable outcomes for red or white = Number of red balls + Number of white balls = 6 + 4 = 10.
- The total number of outcomes = 15 (total balls).

**Probability of drawing a red or white ball = (Number of favorable outcomes) / (Total outcomes) = 10 / 15 = 2 / 3 (after simplification)**

### Summary of Results:
1. Probability of drawing a white ball = **4/15**
2. Probability of drawing a red ball = **2/5**
3. Probability of drawing a ball that is not black = **2/3**
4. Probability of drawing a red or white ball = **2/3**

---