1. Definition: Mathematical or Random Experiments – any procedure or process of obtaining a set of observations which may be repeated under basically the same conditions which lead to well – defined outcomes. Examples: Tossing of a Coin Rolling a die Definition: Sample Space – the set of all possible outcomes in a mathematical or random experiment. Definition: Event – any subset of the sample space.

2. Example: Consider the experiment of rolling a die. Then, the sample space S is the set . Now, define the following events as follows: E 1 = event of getting a prime number E 2 = event of getting an odd number E 3 = event of getting an even number

3. Definition: Let S be a sample space and let A be any event of S. The probability of A denoted by P(A) is a real number satisfying the following axioms: i) ii) P(S) = 1 iii) If A and B are mutually exclusive, then . From the preceding axiom, the following results are immediate: i) If is a null event, then . ii) If is the complement of an event A , then . iii) If A and B are any events, then .