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)

$\frac{5}{21}$

Answer 2

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