In a simple example I tried to use TransformedDistribution to define a probability distribution of a variable that is +/- 1 with probability 1/2. Doing so results in an extraneous value in the resulting PDF.
z = TransformedDistribution[2 x - 1, x \[Distributed] BinomialDistribution[1, 1/2]]
PDF[z][Range[-2, 2]]
{0, 1/2, 2/\[Pi], 1/2, 0}
There does not seem to be a problem in defining the Binomial distribution for a single trial.
w = TransformedDistribution[x, x \[Distributed] BinomialDistribution[1, 1/2]];
PDF[w][Range [-1, 2]]
{0, 1/2, 1/2, 0}
I am running Mathematica Home Edition version 10.0.2