Axioms of Probability
Consider an experiment whose sample space is S. For each event E of the sample space S, we assume that a number P(E) is defined and satisfies the following three axioms.
Axiom-1: 0 ≤ P(E) ≤ 1
Axiom-2: P(S) = 1
Axiom-3: For any sequence of mutually exclusive events E1, E2, …(that is, events for which Ei ∩ Ej = φ when i ≠ j
Odds in Favour and Odds Against
In an event E, if the total number of possibilities of favorable cases is ‘a’ and the total number of unfavorable cases is ‘b’.
then, odds in favour = a/b and odds against = b/a
If a + b is sample space, then
P(E) = Odds in favor / Odds in favour + odds against
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