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If some of the audience fell asleep for some of this talk, what was the average proportion of the talk that people heard?
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Problem



When a speaker gave a talk, 6% of the audience slept through the whole thing.

22% of the audience stayed awake and heard the entire talk.

Of the rest of the audience, half of them heard $\frac{2}{3}$ of the talk, and half of them heard $\frac{1}{3}$ of the talk.

What was the average proportion of the talk that people heard?

This problem is adapted from the World Mathematics Championships