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Question
A bag contains 5 brown and 4 white socks. A man pulls out two socks. The probability that these are of the same colour is
Options
\[\frac{5}{108}\]
\[\frac{18}{108}\]
\[\frac{30}{108}\]
\[\frac{48}{108}\]
Solution
\[ \frac{48}{108}\]
\[P\left( \text{ same coloured socks }\right) = P\left( \text{ both brown } \right) + P\left( \text{ both white } \right)\]
\[ = \frac{5}{9} \times \frac{4}{8} + \frac{4}{9} \times \frac{3}{8}\]
\[ = \frac{20}{72} + \frac{12}{72}\]
\[ = \frac{32}{72}\]
\[ = \frac{4}{9} = \frac{48}{108}^{}\]
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