Suppose three versions of a quiz are given to a large class. One half of the students were given Version A, one quarter were given Version B, and one quarter were given Version C. The pass rate for Version A was 50%, the pass rate for Version B was 82%, and the pass rate for Version C was 85%. Suppose you ask a student from the class at random if they passed the quiz. If the student answers truthfully that they passed, then what is the probability they took Version A of the quiz? Give the probability to six decimal places.

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