Intuitively, if entropy formula_73 is regarded as a measure of uncertainty about a random variable, then formula_75 is a measure of what formula_2 does "not" say about formula_3. This is "the amount of uncertainty remaining about formula_3 after formula_2 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in formula_3, minus the amount of uncertainty in formula_3 which remains after formula_2 is known", which is equivalent to "the amount of uncertainty in formula_3 which is removed by knowing formula_2". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.