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![**Problem: Conditional Probability and Partition of Sample Space**
Events \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of a sample space \( S \) with \( P(A_2) = 0.39 \). If \( E \) is an event in \( S \) with \( P(E \mid A_1) = 0.12 \) and \( P(E \mid A_2) = 0.18 \), compute \( P(A_2 \mid E) = ? \)
**Hint:** Because \( A_1 \) and \( A_2 \) are mutually exclusive and form a complete partition of the sample space, \( P(A_1) = 1 - P(A_2) \).
**Note:** If your final answer has up to four decimal places, please enter your full answer without rounding it. If your answer contains more than four decimal places, please round it to four decimal places before entering it in the box below.
[Answer Box]](https://content.bartleby.com/qna-images/question/fa413bcf-f4d4-4563-8c5c-bfbbe2a7d62c/dc9b1958-f06d-418b-975e-f9552984eb23/z26t1zm_processed.png)
