Ω means an inevitable event, so here a =ω Ω and B =ωB, of course, it means that an event and an inevitable event together (whether before or after) will not change or affect the probability of its occurrence.

That is to say, the probability is still the same, which can be regarded as the same thing as the original event.

Total probability theorem

The total probability formula is an important formula in probability theory, which transforms the probability solution of a complex event A into the probability summation of a simple event in different situations.

Content: If events B 1, B2, B3…Bn form a complete event group, that is, they are incompatible with each other, their sum is a complete set; And P(Bi) is greater than 0, which holds for any event a.

P(A)= P(A | b 1)P(b 1)+P(A | B2)P(B2)+...+ P(A|Bn)P(Bn).

Or: p (a) = p (ab1)+p (ab2)+...+p (ABN)), where the relationship between a and BN is intersection.