Set Theory, Combinatorics & Probability Theory

Probability is the ratio of total numbers of elements of two sets namely set of favorable cases and set of total cases. For discrete random variable these sets are countable. For a continuous random variable these are uncountable and infinite. Set operators like union, intersection, complement and difference are used. Venn diagram helps visualize sets and various operations on such sets. For large countable set generated from multiple discrete random variables, we also use counting techniques also called Combinatorics. This is used in the calculation of probability of an event. Here we can find all the possible arrangements (permutation) and selections (combinations) of multiple discrete random variables for the computation of probability of an event. This value of probability can also be obtained by listing down all the possible outcomes. But this process is tedious and time consuming. So Combinatorics uses formula of permutation and combination for quick computation of such probabilities.