Five   horses are in  a race. Mr. A selects two of the horses at random and on them. the probability that   Mr. A selected the winning horse is

Let 5 horses are ${\mathrm{H}}_{1,}{\mathrm{H}}_2,{\mathrm{H}}_3,{\mathrm{H}}_4\text{ and }{\mathrm{H}}_5$  total ways of selecting pair of horses be

${=}^5{C}_2=\left[\text{ i.e. }{H}_1{H}_2;H_1{H}_3;H_1{H}_4;H_1{H}_5\right]H_2{H}_3;H_2{H}_4;H_2{H}_5;H_3{H}_5;H_4{H}_5$

Favourable cases for each horse to  win   the race is   4 ways $\left(\text{ e.g.for }{H}_1:H_1{H}_2,H_1{H}_3,H_1{H}_4,H_1{H}_5\right.\text{ ) }$

Hence required probability $\frac{4}{10}=\frac{2}{5}$