Does the success of a prey population
depend on its predators? explain.

Yes very much so. Let's say the prey were snakes. The predators were birds. If many of the birds were wiped out, there are barely any limiting factors maintaining the snake population. The snake population can overpopulate and affect other species. If there were an abundance of birds, the snake population would decrease immensely, but then the bird population will soon run out of snakes and starve. This will then cause the bird population to suffer. As you can tell, both the prey and predator population effect each other immensely. 

The moths will eventually become extinct