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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?
~~>![Image alt text](https://math.codidact.com/uploads/QXFghvR3D4g399S4fE9yqGLT)~~
Blitzstein, *Introduction to Probability* (2019 2 ed), Chapter 1, p 60.
~~![Image alt text](https://math.codidact.com/uploads/go7h9pBMeE76oAGvSeQGGvXR)~~
Bertsekas, *Introduction to Probability* (2008 2e), p 32, Fig. 1.14.

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.
![Diagram](https://math.codidact.com/uploads/go7h9pBMeE76oAGvSeQGGvXR)
Bertsekas, *Introduction to Probability* (2008 2e), p 32, Fig. 1.14.

probability visualization