How can I visualize the Law of Total Probability with extra conditioning?

How can I pictorialized this Theorem 2.4.3? As you can see below, I edited a picture by drawing E inside B.. Is my edit correct? Can my edit be improved?

Theorem 2.4.3 (LOTP with extra conditioning). Let $A_{1}, \ldots, A_{n}$ be a partition of S. Provided that $P\left(A_{i} \cap E\right)>0$ for all $i$, we have $$ P(B \mid E)=\sum_{i=1}^{n} P\left(B \mid A_{i}, E\right) P\left(A_{i} \mid E\right) $$

Blitzstein, Introduction to Probability (2019 2 ed), Chapter 1, p 60.

Bertsekas, Introduction to Probability (2008 2e), p 32, Fig. 1.14.

posted almost 4 years ago

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3y ago by Wolgwang‭

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