Mathematics - Probability Question with Solution | TestHub

Probability of getting sum of selected two numbers is even $=P\left(E_1\right)=\frac{{}^5{C}_2+{}^5{C}_2}{{}^{11}{C}_2}$ Probability of getting sum is even and selected numbers are also even $P\left(E_2\right)=\frac{{}^5{C}_2}{{}^{11}{C}_2}$ Hence, $P\left(\frac{E_2}{E_1}\right)=\frac{{}^5{C}_2}{{}^6{C}_2+{}^5{C}_2}=\frac{10}{15+10}=\frac{2}{5}$.