Another interpretation of the KL divergence is the "unnecessary surprise" introduced by a prior from the truth: suppose a number "X" is about to be drawn randomly from a discrete set with probability distribution . If Alice knows the true distribution , while Bob believes (has a prior) that the distribution is , then Bob will be more surprised than Alice, on average, upon seeing the value of "X". The KL divergence is the (objective) expected value of Bob's (subjective) surprisal minus Alice's surprisal, measured in bits if the "log" is in base 2. In this way, the extent to which Bob's prior is "wrong" can be quantified in terms of how "unnecessarily surprised" it is expected to make him.