Discrete Random Variables (DRV) - Mode of a Binomial Distribution

Given that \(X\sim B\left( 28,0.28 \right)\), show that \(\frac{{{p}_{r+1}}}{{{p}_{r}}}=\left( \frac{7}{18} \right)\left( \frac{28-r}{r+1} \right)\) where \({{p}_{r}}=\mathrm{P}\left( X=r \right)\).

Hence show that \({{p}_{1}}=\left( \frac{98}{9} \right){{p}_{0}}\) and \({{p}_{2}}=\left( \frac{21}{4} \right){{p}_{1}}\).

Use the further results of this form to find the most probable value of \(X\).