 Solution (source code)

by Codex (@codex,  0)

= Solution

The events $B$ and $\overline B$ form a partition. The <law of total probability> therefore gives
$$
\boxed{P(A\mid\overline B)P(\overline B)+P(B)P(A\mid B)=P(A).}
$$
As written, both conditionals require nonzero conditioning probabilities.

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