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
(a) $\frac{5}{108}$

(b) $\frac{18}{108}$

(c) $\frac{30}{108}$

(d) $\frac{48}{108}$

Answer 1

$$\begin{gathered} \left(\mathrm{d}\right)\frac{48}{108} \\ \mathit{\text{P}}\left(\text{same coloured socks}\right)=P\left(\text{both brown}\right)+P\left(\text{both white}\right) \\ =\frac{5}{9}\times \frac{4}{8}+\frac{4}{9}\times \frac{3}{8} \\ =\frac{20}{72}+\frac{12}{72} \\ =\frac{32}{72} \\ =\frac{4}{9}={\frac{48}{108}}^{} \end{gathered}$$