Mathematics - Probability Question with Solution | TestHub

Let $A\equiv$ event of two socks being brown. $\mathrm{B}\equiv$ event of two socks being white. $$\text{ Then }\begin{array}{rl}& P(A)=\frac{{}^5{C}_2}{{}^9{C}_2}=\frac{5.4}{9.8}=\frac{5}{18},\mathrm{P}(\mathrm{B})\\ & =\frac{{}^4{\mathrm{C}}_2}{{}^9{\mathrm{C}}_2}=\frac{4.3}{9.8}=\frac{3}{18}\end{array}$$ Now, since $\mathrm{A}$ and $\mathrm{B}$ are mutually exclusive events, so required probability $$=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=\frac{5}{18}+\frac{3}{18}=\frac{4}{9}$$