Much of what we do is based on the belief that the future is largely unpredictable. Very few people would play games such as roulette or the lottery, or buy and sell insurance policies if the outcomes were known in advance. Probability is the study of chance and attempts to express quantitatively and qualitatively ideas of uncertainty. The theory of probability involves mathematics, logic, and considerations of the underlying physical mechanisms that cause variability.
In many applications the concepts are easy and the results are
consistent with intuition, however in some cases it is more difficult and following our intuition can lead to contradictions. It is for this reason that we need a formal consistent mathematical theory of probability.