Meaning of certain event | Babel Free

Definitions

1. An event that contains all of the possible outcomes and thus is known a priori to be certain to occur;
2. An event that contains all of the possible outcomes and thus is known a priori to be certain to occur; (more formally) the entire sample space (which by definition has measure 1 and probability 1); said sample space with the exclusion of, at most, a set of measure 0 (thus retaining measure 1).
3. the entire sample space (which by definition has measure 1 and probability 1); said sample space with the exclusion of, at most, a set of measure 0 (thus retaining measure 1).

Examples

“Measure 0 is assigned to an impossible event, and measure 1 is assigned to a certain (sure) event. A certain event is denoted as #92;Omega; an impossible event, as #92;empty.”

“Hence the event A#95;1#92;capA#95;2#92;cap#92;dots#92;capA#95;k will be a certain event too, i.e. P(A#95;1#92;capA#95;2#92;cap#92;dots#92;capA#95;k)#61;1.”

“In probability theory, events are sets with a non-negative length that is at most one, since we assume that the sample space #92;Omega is the certain event and should be assigned the largest length, i.e., 1 (probability 100%).”

CEFR level