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Logistic regression cut point

Is it possible to change the cut point used in logistic regression for generating the Most Likely (outcome) category? I read somewhere that the cut point was .5, but can this value be changed, and if so, how?

Thanks in advance -
Let's say you have a response with two levels, A or B. The predicted values for logistic regression are probabilities for the two levels. When you do a logistic regression in JMP, and save the formulas, it creates a column called "Most Likely...". This column does not use a cutoff, but simply identifies the response level with the highest predicted probability. For example, if the predicted probability for level A is 0.72, then the predicted probability for level B is 0.28. The Most Likely level is A.