There are 7 red, 5 black and 3 white balls in a bag. A ball is drawn at random. Find the probability that ball drawn is:
(i) white
(ii) not white
(iii) either red or white.

Explanation

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

### Given:
- Number of red balls = 7
- Number of black balls = 5
- Number of white balls = 3

### Total number of balls:
\[ \text{Total balls} = \text{Number of red balls} + \text{Number of black balls} + \text{Number of white balls} = 7 + 5 + 3 = 15 \]

### (i) Probability that the ball drawn is white:
The number of white balls is 3. The probability \( P(\text{white}) \) can be calculated as:
\[ P(\text{white}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{3}{15} = \frac{1}{5} \]

### (ii) Probability that the ball drawn is not white:
To find the probability that the ball drawn is not white, we can use the complement rule:
\[ P(\text{not white}) = 1 - P(\text{white}) = 1 - \frac{1}{5} = \frac{4}{5} \]

### (iii) Probability that the ball drawn is either red or white:
The number of red balls is 7 and the number of white balls is 3. The total number of balls that are either red or white is:
\[ \text{Number of red or white balls} = \text{Number of red balls} + \text{Number of white balls} = 7 + 3 = 10 \]
The probability \( P(\text{red or white}) \) can be calculated as:
\[ P(\text{red or white}) = \frac{\text{Number of red or white balls}}{\text{Total number of balls}} = \frac{10}{15} = \frac{2}{3} \]

### Final Answers:
(i) Probability that the ball drawn is white: \( \frac{1}{5} \)

(ii) Probability that the ball drawn is not white: \( \frac{4}{5} \)

(iii) Probability that the ball drawn is either red or white: \( \frac{2}{3} \)

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