A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red ? (ii) white ? (iii) not green? PROBABILITY 215
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
$$N = 5\text{ (red)} + 8\text{ (white)} + 4\text{ (green)} = 17$$
2. (i) Probability of drawing a red marble
- Favourable outcomes = 5 (red marbles)
- $$P(\text{red}) = \frac{5}{17}$$
3. (ii) Probability of drawing a white marble
- Favourable outcomes = 8 (white marbles)
- $$P(\text{white}) = \frac{8}{17}$$
4. (iii) Probability of NOT drawing a green marble
- Marbles that are not green = red + white = 5 + 8 = 13
- $$P(\text{not green}) = \frac{13}{17}$$
All fractions are already in their simplest form.
Correct Answer: (i) \(\frac{5}{17}\) , (ii) \(\frac{8}{17}\) , (iii) \(\frac{13}{17}\)