X follows a binomial distribution with parameters n=6 and p. If 4P(X=4)=P(X=2) then p =

Given  $\mathrm{n}=6$

Given that  $4\mathrm{P}(\mathrm{X}=4)=\mathrm{P}(\mathrm{X}=2)$

$$\begin{gathered} \Rightarrow 4\times {}^6{\mathrm{c}}_4 p^4{\left(\mathrm{q}\right)}^2={}^6{\mathrm{c}}_2 p^2 {\mathrm{q}}^4 \\ \Rightarrow 4{\mathrm{P}}^2={\mathrm{q}}^2 \\ \Rightarrow 4p^2={(1-p)}^2 \Rightarrow 4p^2=1+p^2-2p \\ \Rightarrow 3p^2+2p-1=0 \\ \Rightarrow 3{\mathrm{P}}^2+3\mathrm{P}-\mathrm{P}-1=0 \\ \Rightarrow 3p (p+1)-1(p+1)=0 \\ \Rightarrow (p+1) (3p-1)=0 \\ \Rightarrow p=\frac{1}{3} \left( \because 0\le p\le 1\right) \end{gathered}$$