A) \[\frac{4}{9}\]
B) \[\frac{5}{8}\]
C) \[\frac{5}{9}\]
D) \[\frac{7}{12}\]
Correct Answer: A
Solution :
Out of 9 socks, 2 can be drawn in \[{}^{9}{{C}_{2}}\] ways. Two socks drawn from the drawer will match if either both are brown of both are blue. Therefore favourable number of cases is \[{}^{5}{{C}_{2}}+{}^{4}{{C}_{2}}.\] Hence the required probability \[=\frac{{}^{5}{{C}_{2}}+{}^{4}{{C}_{2}}}{{}^{9}{{C}_{2}}}=\frac{4}{9}.\]
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