 Solution (source code)

by Codex (@codex,  0)

= Solution

Insert the values from (a) into <Bayes' theorem>:
$$
\frac{P(A\mid B)P(B)}{P(A)}
=\frac{(4/5)(5/9)}{13/18}=\frac8{13}=P(B\mid A).
$$
Thus the identity is \b[satisfied]. Equivalently, both $P(A\mid B)P(B)$ and $P(B\mid A)P(A)$ equal the joint <probability> $4/9$.

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