Pr[infested] = 0.25

Pr[!infested] = 0.75

The probabilities of the scanner behavior is

Pr[infested|infested] = 0.8

Pr[pest free|infested] = 0.2

Pr[infested|!infested] = 0.2

Pr[pest free|!infested] = 0.8

So Pr[pest free] = Pr[pest free|infested]Pr[infested] + Pr[pest free|!infested]Pr[!infested]

Pr[pest free] = 0.2*0.25 + 0.8*0.75 = 0.65

and so with a 100 tree sample we expect that 0.65*100 = 65 trees will register as pest free by the scanner.

So you are correct, though you sort of stumbled to the answer.