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If $X$ follows a binomial distribution with parameters $n=6$ and $\quad p$ and $4(P(X=4))=P(X=2)$, then $p=$
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Verified Answer
The correct answer is:
$\frac{1}{3}$
$4 P(X=4)=P(X=2) \Rightarrow 4 .{ }^6 C_4 p^4 q^2={ }^6 C_2 p^2 q^4$
$\Rightarrow 4 p^2=q^2 \Rightarrow 4 p^2=(1-p)^2$
$\Rightarrow 3 p^2+2 p-1=0 \Rightarrow p=\frac{1}{3}$
$\Rightarrow 4 p^2=q^2 \Rightarrow 4 p^2=(1-p)^2$
$\Rightarrow 3 p^2+2 p-1=0 \Rightarrow p=\frac{1}{3}$
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