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

Let 5 horses are  $H_1,H_2,H_3,H_{4}and{H}_5$ Total ways of selecting pair of horses be
$\begin{array}{l}{=}^5{C}_2=10[i.e.H_1{H}_2,H_1{H}_3,H_1{H}_4,H_1{H}_5,\\ H_2{H}_3,H_2{H}_4,H_2{H}_5,H_3{H}_4,H_3{H}_5,H_4{H}_5]\end{array}$
Any horse can win the race in 4 ways $(e.g.for{H}_1:H_1{H}_2,H_1{H}_3,H_1{H}_4,H_1{H}_5)$  Hence required probability  $=\frac{4}{10}=\frac{2}{5}$