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Question
An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
Options
\[\frac{5}{84}\]
\[\frac{3}{9}\]
\[\frac{3}{7}\]
\[\frac{7}{17}\]
Solution
\[ \frac{5}{84}\]
\[\text{ Given }: \]
\[\text{ Red balls} = 2\]
\[\text{ Blue balls} = 3\]
\[\text{ Black balls } = 4\]
\[P\left( \text{ all three balls are of same colour } \right) = P(\text{ all three are blue } ) + P\left( \text{ all three are black } \right)\]
\[ = \frac{3}{9} \times \frac{2}{8} \times \frac{1}{7} + \frac{4}{9} \times \frac{3}{8} \times \frac{2}{7}\]
\[ = \frac{1}{84} + \frac{4}{84}\]
\[ = \frac{5}{84}\]
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