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

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

KCETKCET 2019Probability

Solution:

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