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

Answer: D

Okay, so this is a binomial experiment, and we can easily translate all of the answer choices to statements about

*H*alone by substituting

*T*= 100 -

*H*.

My inclination is to approximate the binomial by a normal distribution, except I don't have a table of values for the GRE. I can sort of make do by drawing a rough picture of a normal distribution with mean 50 and comparing areas, though. Doing this, I see that (E) is really small and (A) is less than (D) -- those are out. More, (C) is less than (D) because in both cases

*H*ranges over five values, but in (D) the density function over that range is greater. This leaves (B) and (D). Depending on what I've drawn, I guess (D), but I'm not sure. Why must we disqualify (B)?