If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1),then the value of$\frac{\mathrm{P}(\mathrm{X}=15)}{\mathrm{P}(\mathrm{X}=18)}-\frac{\mathrm{P}(\mathrm{X}=16)}{\mathrm{P}(\mathrm{X}=17)}$is equal to

n = 33, let probability of success is p and q = 1 - p
3p(x = 0) = p(x =1)
$\begin{array}{c}{\text{ 3. }}^{33}{\mathrm{C}}_0(\mathrm{q}{)}^{33}{=}^{33}{\mathrm{C}}_1{\mathrm{pq}}^{32}\\ \Rightarrow 3(\mathrm{q}{)}^{33}=33\left({\mathrm{pq}}^{32}\right)\\ \Rightarrow q=11p\therefore 1-p=11p\\ \mathrm{p}=\frac{1}{12},\mathrm{q}=\frac{11}{12},\frac{\mathrm{q}}{\mathrm{p}}=11\\ \frac{\mathrm{p}(\mathrm{x}=15)}{\mathrm{p}(\mathrm{x}=18)}-\frac{\mathrm{p}(\mathrm{x}=16)}{\mathrm{p}(\mathrm{x}=17)}\\ \frac{{ }^{33}{\mathrm{C}}_{15}{\mathrm{p}}^{15}{\mathrm{q}}^{18}}{{ }^{33}{\mathrm{C}}_{18}{\mathrm{p}}^{18}{\mathrm{q}}^{15}}-\frac{{ }^{33}{\mathrm{C}}_{16}{\mathrm{p}}^{16}{\mathrm{q}}^{17}}{{ }^{33}{\mathrm{C}}_{17}{\mathrm{p}}^{17}{\mathrm{q}}^{16}}={\left(\frac{\mathrm{q}}{\mathrm{p}}\right)}^3-\left(\frac{\mathrm{q}}{\mathrm{p}}\right)\\ =(11{)}^3-11\\ =1320\end{array}$