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:

Total ways to select 2 horses from 5 = ${}^5{C}_2=10$.
Number of ways to select the winning horse (which is 1 specific horse) and 1 other horse from the remaining 4:
Ways = ${}^1{C}_1\times {}^4{C}_1=4$.
Probability $P=\frac{4}{10}=\frac{2}{5}$.