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Question
A bag contains 3 white, 4 red and 5 black balls. Two balls are drawn one after the other, without replacement. What is the probability that one is white and the other is black?
Solution
\[\text{ Given : Box }=\left( 3 W+4R+5B \right) \text{ balls } \]
\[P\left( \text{ one white and one black } \right) = P\left( \text{ first white and second black } \right) + P\left( \text{ first black and second white } \right)\]
\[ = \frac{3}{12} \times \frac{5}{11} + \frac{5}{12} \times \frac{3}{11}\]
\[ = \frac{15}{132} + \frac{15}{132}\]
\[ = \frac{30}{132}\]
\[ = \frac{5}{22}\]
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