First, you can rewrite the inequality in the prompt:

(1/2)n - 2 >= 0

(1/2) n >= 2

n >= 4

So the question really asks for the probability that n >= 4.

(1) doesn't tell you anything, because we don't know what integers are in the hat.

(2) also doesn't tell you anything, because although we know every number in the hat is between 1 and 30 inclusive, we don't know how many are equal to 4 or greater.

(1) and (2) together still don't tell you anything. We know there are 6 integers in the hat, and we know that all of the integers are between 1 and 30 inclusive, but there's no way of telling how many of the integers are greater than or equal to 4.