In a school there are 3 sections $A, B$ and $C$. Section $A$ contains 20 girls and 30 boys, section $B$ contains 40 girls and 20 boys and section $C$ contains 10 girls and 30 boys. The probabilities of selecting the section $A, B$ and $C$ are $0.2,0.3$ and 0.5 respectively. If a student selected at random from the school is a girl, then the probability that she belongs to section $A$ is

If the probability distribution of a random variable $X$ is as follows, then the mean of $X$ is

$$ \begin{array}{ccccc} \hline \boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}} & -1 & 0 & 1 & 2 \\ \hline \boldsymbol{P}\left(\boldsymbol{X}=\boldsymbol{x}_{\boldsymbol{i}}\right) & \boldsymbol{k}^3 & 2 \boldsymbol{k}^3+\boldsymbol{k} & 4 \boldsymbol{k}-10 \boldsymbol{k}^2 & 4 \boldsymbol{k}-1 \\ \hline \end{array} $$

If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2)=$