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We are testing a statistical hypothesis about an experiment that can have 3 possible outcomes. Suppose...

We are testing a statistical hypothesis about an experiment that can have 3 possible outcomes. Suppose that αi is the probability of not detecting outcome i, i = 1, 2, 3 when this outcome has in fact occurred. Find the conditional probability that the outcome is i = 1, 2, 3 if our test has not detected outcome 1.

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