:drool:
Following Zaffy's lead (and assuming we're not dealing with psychological factors per dun), I figure as follows:
If you line up the 23 people in a row and have them each pick silently and then reveal, your total # of combinations is 4^23. The combinations we're interested in are those where exactly one "D" is picked, so we can break that up into: combos where person 1 picked "D" and no one else did + combos where person 2 picked "D" and no one else did + etc.
# of combos where p1 picks "D" alone = 1*3^22 ("D" is fixed, and then the rest pick from "A", "B", and "C"). The # of combinations is the same for all, so the total # of combinations where one person picks "D" is: 23*3^22
Therefore p = (23*3^22) / (4^23) = 0.01026 = 1.026%
or in general, for N people, p = (N*3^(N-1) / (4^N)
Checking for small cases, with N = 1, p = 1/4 as expected,
with N = 2, p = 6/16 as expected (AD, BD, CD, DA, DB, DC)
...woot!
