Question

If ‘X’ has a binomial distribution with parameters n = 6, p and P(X = 2) = 12, P(X = 3) = 5 then P =

• A. $\frac{1}{2}$
• B. $\frac{5}{21}$
• C. $\frac{5}{16}$
• D. $\frac{1}{5}$

Answer 1

Answer: (B)

$n=6$
$P\left(x=r\right){=}^n{C}_r{q}^{n-r}{p}^r$
$P\left(x=2\right)=12$
${}^6{C}_2{q}^4{p}^2=12\dots \left(1\right)$
$P\left(x=3\right)=5$
${}^6{C}_3{q}^3{p}^3=5\dots \left(2\right)$
$\frac{\left(1\right)}{\left(2\right)}\Rightarrow \frac{{}^6{C}_2{q}^4{p}^2}{{}^6{C}_3{q}^3{p}^3}=\frac{12}{5}$
$\frac{15q}{20p}=\frac{12}{5}$
$75q=240P$
$75\left(1-p\right)=240p$
$75-75p=240p$
$75=315P$
$p=\frac{75}{315}=\frac{5}{21}$