Question: In classification, if we are applying a trained model to previously unseen test observations, we calculate the posterior probability P(Y=y | X=x) for each observation

In classification, if we are applying a trained model to previously unseen test observations, we calculate the posterior probability P(Y=y | X=x) for each observation and assign the observation to y=1 if the probability is above some threshold t. As t decreases towards 0, should we expect precision to decrease or increase? Explain your answer.

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