Discussion
A box contains 4 black, 3 red and 6 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
Answer: B
The box holds \( 4 + 3 + 6 = 13 \) marbles.
\[ \text{total ways} = {}^{13}C_{2} = 78 \]
\[ \text{same colour} = {}^{4}C_{2} + {}^{3}C_{2} + {}^{6}C_{2} = 6 + 3 + 15 = 24 \]
\[ P = \frac{24}{78} \]
The three colours are mutually exclusive, so their counts add before dividing.
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