 |
| Probability of an Event |
|
| So far, we have introduced the sample of an experiment and used it to describe events. In this section, we introduce probabilities associated to the events. |
| |
| If a trial results in n-exhaustive, mutually exclusive and equally likely cases and m of them are favourable to the occurrence of an event A, then the probability of the happening of A, denoted by P(A), is given by |
| |
 |
| |
 |
| |
| Note 2: If P(A) = 0 then A is called a null event, or impossible event. |
| |
| Note 3: If P(A) = 1 then A is called a sure event. |
| |
| Note 4: If m is the number of cases favourable to A. Then |
| |
| m - n is favourable to "non occurrence of A". |
| |
 |
| |
| Note 5: If the odds are a:b in favour of A then |
| |
| |
 |
| |
| This is the same as odds are b:a against the event A. |
| |
|
| |
If a trial is repeated N number of times under essential homogeneous  |
| |
 |
| |
|
| |
| Axiomatic approach to probability closely relates the theory of probability to set theory. |
| |
| Let S be the sample space of an experiment. Probability is a function, which associates a non-negative real number to every event A of the sample space denoted by P(A) satisfying the following axioms. |
| |
 For
every event A in S, P(A) ³ 0. |
| |
|
P(S) = 1. |
| |
|
If A1, A2, A3,….An are mutually exclusive events in S, then |
| |
 |
| |
