let B be a subset of A. use axioms of probability to explain the relation between PA and PB.
Given that, Then, Where
The axioms of probability are, 1) For any event A, (Non-negativity)
2) (Norm)
3) If A1, A2,...,An are mutually exclusive events then,
Now, (From Axiom 3)
As, (From Axiom 1)
This is the relationship between P(A) and P(B) when B is a subset of A
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