is there any concept like "cost of misclassification" relating to Probit/ logit model?

as we know the purpose of logit/probit models is to predict the probability of the group membership of an observation, if the observation is misclassified by the model, it indicates poor predictability of the model.

can we quantify such poor predictabilities in terms of misclassifcation of the observations?

if so, how to do it?

thanks in advance

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