A contest will consist of n questions, each of which is to be answered either "True" or "False." Anyone who answers all n questions correctly will be a winner. What is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1,000
(A) 5
(B) 10
(C) 50
(D) 100
(E) 1,000
