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Question
A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.
Solution
\[\text{ Given } :\]
\[\text{ Bag } 1=\left( 3W+6B \right) \text{ balls } \]
\[ \text{ Bag } 2=\left( 5B+4W \right)\text{ balls } \]
\[P\left( \text{ balls of same colour are drawn } \right) = P\left( \text{ both black } \right) + P\left( \text{ both white } \right)\]
\[ = \frac{6}{9} \times \frac{5}{9} + \frac{3}{9} \times \frac{4}{9}\]
\[ = \frac{30}{81} + \frac{12}{81}\]
\[ = \frac{42}{81}\]
\[ = \frac{14}{27}\]
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