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(D) The probability mass function for a binomial distribution is given by $P(X=r) = {}^{n}C_{r} q^{n-r} p^{r}$,where $q = 1-p$.Given $n=6$,we have:$P(

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(D) The probability mass function for a binomial distribution is given by $P(X=r) = {}^{n}C_{r} q^{n-r} p^{r}$,where $q = 1-p$.Given $n=6$,we have:$P(X=2) = {}^{6}C_{2} q^{4} p^{2} = 15 q^{4} p^{2} = 12$  (Equation $1$)$P(X=3) = {}^{6}C_{3} q^{3} p^{3} = 20 q^{3} p^{3} = 5$  (Equation $2$)Dividing Equation $1$ by Equation $2$:$\frac{15 q^{4} p^{2}}{20 q^{3} p^{3}} = \frac{12}{5}$$\frac{3q}{4p} = \frac{12}{5}$$15q = 48p$$5q = 16p$Since $q = 1-p$,we substitute:$5(1-p) = 16p$$5 - 5p = 16p$$5 = 21p$$p = \frac{5}{21}$

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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