A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i) red ? (ii) not red?
Step-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) / (Total number of equally likely outcomes). For complementary events, P(not A) = 1 – P(A).
Step 1: Identify the total number of balls in the bag.
$$\text{Total balls}=3\text{ (red)}+5\text{ (black)}=8.$$
Step 2: (i) Probability of drawing a red ball.
- Favourable outcomes = number of red balls = 3.
- Total outcomes = 8.
Thus,
$$P(\text{red})=\frac{\text{Number of red balls}}{\text{Total balls}}=\frac{3}{8}.$$
Step 3: (ii) Probability of drawing a ball that is not red (i.e., black).
- This is the complement of the event "red".
- Using the complement rule,
$$P(\text{not red})=1-P(\text{red})=1-\frac{3}{8}=\frac{5}{8}.$$
Alternatively, directly count the black balls:
Number of black balls = 5, so
$$P(\text{not red})=\frac{5}{8}.$$
Thus the required probabilities are $\frac{3}{8}$ and $\frac{5}{8}$ respectively.
Correct Answer: (i) $\frac{3}{8}$, (ii) $\frac{5}{8}$