It's easier to solve for the opposite of what the question is asking for when you see the term "at least." The opposite of at least one tail is no heads. The only way zero heads will result is if each of the four flips results in a tail:
p = (1/2)(1/2)(1/2)(1/2) = 1/16

That's the opposite of the answer, so subtract it from 1:
p = 1 - 1/16=15/16, choice (E).