Question
Events $E_1$ and $E_2$ form a partition of the sample space $S$. $A$ is any event such that $P(E_1) = P(E_2) = \frac{1}{2}$, $P(E_2 \mid A) = \frac{1}{2}$, and $P(A \mid E_2) = \frac{2}{3}$. Then, $P(E_1 \mid A)$ is
Events $E_1$ and $E_2$ form a partition of the sample space $S$. $A$ is any event such that $P(E_1) = P(E_2) = \frac{1}{2}$, $P(E_2 \mid A) = \frac{1}{2}$, and $P(A \mid E_2) = \frac{2}{3}$. Then, $P(E_1 \mid A)$ is