Aparticular bird species found in north america obtains most of its food energy by catching and eating insects. a mutation arises in this bird population that increases the length of its beak. although many mutations are harmful, this particular mutation has increased the ability of the bird to catch and eat certain insects. which of these is the most likely outcome of this mutation

The answer is: the new trait will be more common in the population.

This is an example of natural selection. In natural selection, genotype variations that will increase the chance of survival and reproduction of some organism are preserved and will be inherited. So, the mutation occurs and it comes out that it is not harmful, but increases the ability of the birds to survive. The birds with the mutation will have greater chance to survive and reproduce than the birds without the mutation. "Mutated" birds will be more likely to pass the new trait to the next generation, and the new trait will be more common in the population.