X : Mr. A selected wining horse

$$\overline X $$ : Mr. A did not select wining horse

Mr. A selected two horses, now probability of not wining the first horse which Mr. A choses = $${4 \over 5}$$

And probability of not wining the second horse also which Mr. A choses = $${3 \over 4}$$ (Here Mr. A out of remaining 4 horses choses one horse among 3 horses which did not win)

$$\therefore$$ $$P(\overline X ) = {4 \over 5} \times {3 \over 4}$$

$$\therefore$$ $$P(X) = 1 - P(\overline X )$$

$$ = 1 - {4 \over 5} \times {3 \over 4}$$

$$ = 1 - {3 \over 5}$$

$$ = {2 \over 5}$$