A number n is chosen at random from
S = {1,2,3,...,50}. Let  $A=\left\{n\in S:n+\frac{{\displaystyle 50}}{{\displaystyle n}}>27\right\},B=\{n\in S:nisaprime\} and C=\{n\in S:nisasquare\}$ Then correct order of their probability is

$\begin{array}{rcl}\mathrm{S}& =& \{1,2,3\dots ,50\}\\ \mathrm{n}\left(\mathrm{S}\right)& =& 50\end{array}$

$\begin{array}{rcl}\mathrm{A}& =& \left\{\mathrm{n}\in \mathrm{S} : \mathrm{n}+\frac{50}{\mathrm{n}}>27\right\}\\ {\mathrm{n}}^2-27\mathrm{n}+50& >& 0 \Rightarrow (\mathrm{n}-2) (\mathrm{n}-25)>0\\ \mathrm{n}& <& 2, \mathrm{n}>25\\ \mathrm{n}& =& \left\{1, 26, 27 .... 50\right\}\\ \mathrm{n}\left(\mathrm{A}\right)& =& 26 \Rightarrow \mathrm{P}\left(\mathrm{A}\right)=\frac{26}{50}\\ \mathrm{B}& =& \left\{\mathrm{n}\in \mathrm{S} : \mathrm{n} \mathrm{is} \mathrm{Prime}\right\}=\{ 2, 3, 4, 7, 11, 13, 17, 19, \\ & & 23, 29, 31, 37, 41, 43, 47 \}\\ \mathrm{P}\left(\mathrm{B}\right) & =& \frac{15}{30}\\ \mathrm{C}& =& \left\{ \mathrm{n}\in \mathrm{S} : \mathrm{n} \mathrm{is} \mathrm{a} \mathrm{Square} \right\}=\left\{1, 4, 9, 16, 25, 36, 49\right\}\\ \mathrm{P}\left(\mathrm{C}\right)& =& \frac{7}{30} \mathrm{P}\left(\mathrm{A}\right)>P\left(\mathrm{B}\right)>\mathrm{P}\left(\mathrm{C}\right)\end{array}$