Question

If X following the Binomial distribution with parameters n=6 and p and 9P (X = 4) = P (X = 2), then p is:

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (A)

$\frac{1}{4}$

$9p(x=4)=p(x=2)$

$9{\times }^6{C}_1{p}^4(1-p{)}^2{=}^6{C}_2{p}^2(1-p{)}^4$

$\frac{9\times 6\times 5}{2}{p}^2=\frac{6\times 5}{2}{\left(1-p\right)}^2$

$p^2=\frac{{(1-p)}^2}{9}$

$\frac{p}{1-p}=\frac{1}{3}$

$3p=1-p$

$4p=1$

$p=\frac{1}{4}$.