A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be (i) white? (ii) blue? (iii) red?
Step-by-Step Solution
Key Concept: Probability of an event = (Number of favourable outcomes) / (Total number of equally likely outcomes). Here each marble is equally likely to be drawn.
1. Total number of marbles
\[\text{Total}=3\text{ (blue)}+2\text{ (white)}+4\text{ (red)}=9\]
2. Probability of drawing a white marble
- Favourable outcomes = 2 (white marbles)
- \[P(\text{white})=\frac{2}{9}\]
3. Probability of drawing a blue marble
- Favourable outcomes = 3 (blue marbles)
- \[P(\text{blue})=\frac{3}{9}=\frac{1}{3}\]
4. Probability of drawing a red marble
- Favourable outcomes = 4 (red marbles)
- \[P(\text{red})=\frac{4}{9}\]
5. Check
- Sum of probabilities = \(\frac{2}{9}+\frac{3}{9}+\frac{4}{9}=\frac{9}{9}=1\), confirming the calculations are correct.
Correct Answer: (i) $\frac{2}{9}$, (ii) $\frac{1}{3}$, (iii) $\frac{4}{9}$