Adopting the Bayesian paradigm, probability theory is a tool to represent incomplete information and to reason in conditions of uncertainty. This chapter, firstly, addresses the algebra of probabilities. What it does is to calculate the probability of an outcome from the probabilities of others. Next, it addresses the problem of encoding information in probability assignments. Probabilities quantify the information about uncertain outcomes (for instance, the outcome of rolling a dice, the value of a quantity, the price of a good, or the state of a system) without any connection to frequencies. Randomness is the epistemic quality we give to an outcome if we do not have enough information to predict it with certainty. Therefore, the adjective random, a synonym of uncertain and opposite to deterministic, will designate those variables whose value we are not capable of predicting. Randomness and probabilities are subjective: the same outcome might be certain to me, but random to you. However, subjective does not mean arbitrary: the same information must correspond to the same probability. Probabilities are epistemically objective.