A bag contains 3 white, 5 black and 2 red balls all of the same shape and size. A ball is drawn at random, find the probability that the ball drawn is :
(i) a black ball (ii) not a red ball.

Answer

To solve the problem step by step, we will find the probability of drawing a black ball and the probability of not drawing a red ball.

### Step 1: Determine the total number of balls in the bag.
- The bag contains:
- 3 white balls
- 5 black balls
- 2 red balls

**Total number of balls = 3 (white) + 5 (black) + 2 (red) = 10 balls.**

### Step 2: Calculate the probability of drawing a black ball.
- The number of favorable outcomes for drawing a black ball is the number of black balls, which is 5.
- The total number of outcomes is the total number of balls, which is 10.

**Probability of drawing a black ball = (Number of black balls) / (Total number of balls) = 5 / 10 = 1 / 2.**

### Step 3: Calculate the probability of not drawing a red ball.
- The number of favorable outcomes for not drawing a red ball includes the white and black balls.
- The number of white balls is 3 and the number of black balls is 5.

**Total number of balls that are not red = 3 (white) + 5 (black) = 8 balls.**

- The total number of outcomes is still 10.

**Probability of not drawing a red ball = (Number of non-red balls) / (Total number of balls) = 8 / 10 = 4 / 5.**

### Final Answers:
(i) The probability of drawing a black ball is **1/2.**
(ii) The probability of not drawing a red ball is **4/5.**

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