MCQ
In a Binomial distribution. $n=4$ and $2 P(X=3)$ $=3 P(X=2)$, then $q=$
- A$\frac{4}{13}$
- B
- C$\frac{11}{13}$
- D$\frac{9}{13}$
(a) : Given $n=4$ and
$
\begin{aligned}
& 2 P(X=3)=3 P(X=2) \\
& \Rightarrow 2\left({ }^4 C_3 p^3 q\right)=3\left({ }^4 C_2 p^2 q^2\right) \\
& \Rightarrow 8 p^3 q=18 p^2 q^2 \Rightarrow 4 p=9 q
\end{aligned}
$
We know that $p=1-q$
$
\Rightarrow 4(1-q)=9 q \Rightarrow q=\frac{4}{13}
$
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