GRE Exam Numerical Ability Probability

A fair coin is to be tossed 100 times, with each toss resulting in a head or a tail. If H is the total number of heads and T is the total number of tails, which of the following events has the greatest probability?
(A) H = 50
(B) T >= 60
(C) 51 =< H =< 55
(D) H >= 48 and T >= 48
(E) H =< 5 or H >= 95

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GRE Other Question

If z = e^(2*Pi*i/5), then 1 + z + z^2 + z^3 + 5z^4 + 4z^5 ++4z^6 + 4z^7 + 4z^8 + 5z^9 = ?
(A) 0
(B) 4e^(3*Pi*i/5)
(C) 5e^(4*Pi*i/5)
(D) – 4e^(2*Pi*i/5)
(E) – 5e^(3*Pi*i)/5 A circular region is divided by 5 radii into sectors. Twenty-one points are chosen in the circular region, none of which is on any of the 5 radii. Which of the following statements must be true?
I. Some sector contains at least 5 of the points.
II. Some sector contains at most 3 of the points.
III. Some pair of adjacent sectors contains a total of at least 9 of the points.
(A) I only
(B) III only
(C) I and II only
(D) I and III only
(E) I, II, and III