  We examine the possible states of subsystems of a system of bits or qubits.
In the classical case (bits), this means the possible marginal distributions of
a probability distribution on a finite number of binary variables; we give
necessary and sufficient conditions for a set of probability distributions on
all proper subsets of the variables to be the marginals of a single
distribution on the full set. In the quantum case (qubits), we consider mixed
states of subsets of a set of qubits; in the case of three qubits, we find
quantum Bell inequalities -- necessary conditions for a set of two-qubit states
to be the reduced states of a single mixed state of three qubits. We conjecture
that these conditions are also sufficient.
