A bag contains 3 red balls and 5 black balls. A ball is drawn at random fret the bag. What is the probability that the ball drawn is (i) red? (ii) not red?

Answer

To solve the problem step by step, we will calculate the probability of drawing a red ball and the probability of drawing a ball that is not red.

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

**Total number of balls = Number of red balls + Number of black balls**
\[ \text{Total balls} = 3 + 5 = 8 \]

### Step 2: Calculate the probability of drawing a red ball.
The probability of an event is given by the formula:
\[ \text{Probability of an event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

For drawing a red ball:
- Number of favorable outcomes (red balls) = 3
- Total number of outcomes = 8

So, the probability of drawing a red ball is:
\[ P(\text{Red}) = \frac{3}{8} \]

### Step 3: Calculate the probability of not drawing a red ball.
The probability of not drawing a red ball can be found using the complement rule:
\[ P(\text{Not Red}) = 1 - P(\text{Red}) \]

From Step 2, we found:
\[ P(\text{Red}) = \frac{3}{8} \]

Thus,
\[ P(\text{Not Red}) = 1 - \frac{3}{8} \]

To perform the subtraction, we convert 1 into a fraction with the same denominator:
\[ 1 = \frac{8}{8} \]

Now we can subtract:
\[ P(\text{Not Red}) = \frac{8}{8} - \frac{3}{8} = \frac{5}{8} \]

### Final Answers:
(i) The probability that the ball drawn is red is \( \frac{3}{8} \).

(ii) The probability that the ball drawn is not red is \( \frac{5}{8} \).

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