Two cards are drawn successively one by one with out replacement from a pack of cards, the mean of number of kings is

$$\begin{gathered} Let X denote the number of King in a draw of two card \\ \Rightarrow P(X=0)=P(no king)=\frac{{48}_{C_2}}{{52}_{c_2}}=\frac{48\times 47}{52\times 51}=\frac{188}{221} \\ \Rightarrow P(X=1)=P(one king and one no king)=\frac{4_{c_1}\times {48}_{C_1}}{{52}_{c_2}}=\frac{2\times 4\times 48}{52\times 51}=\frac{32}{221} \\ \Rightarrow P(X=2)=P(two king)=\frac{4_{c_2}}{{52}_{c_2}}=\frac{4\times 3}{52\times 51}=\frac{1}{221} \\ Probability of distribution \Rightarrow Mean of X=\sum _{n=0}^2{x}_{i}p\left(x_i\right) \\ =0\times \frac{188}{221}+1\times \frac{32}{221}+2\times \frac{1}{221}=\frac{34}{221}=\frac{2}{13} \\ \mathrm{nP}=\frac{2}{13} \end{gathered}$$