All business is, to a greater or lesser extent, concerned with the taking of risk. This paper attempts to explain some of the main approaches that have been adopted in pursuing the concept of risk from a probabilistic viewpoint. The word ‘risk’ itself has been used fairly indiscriminately by writers, and thus gets given a number of different senses, but it has attained a clear and precise definition at various times and in different types of literature. Indeed we can distinguish three main avenues of development. The first is the pure economic concept, the second the actuarial approach, and the third the more recent linkage of risk analysis with the general approach to decision-making under uncertainty.