# Threshold to build confusion matrix?

I a have data set with 10 sections of data and each section shows one day observation. I designed the training and test set as follows: 8 sections for training the data and the last two sections for the test set. In this case, we have a binary (Male/Female) classification problem, so we applied different classifiers (e.g., naive bayes, decision tree and bayesian network) to predict the output. After applying the classifier on the training set and feeding the test set to assess the performance of each classification algorithm, we obtained such probabilities for each class (male/female).

For example for Naive bayes:

    prob(Male)  prob(Female)   prediction
0.3         0.70           ?
0.45        0.55           ?
0.67        0.33           ?
0.52        0.48           ?


For Decision Tree:

    prob(Male)  prob(Female)   prediction
0.4         0.60           ?
0.65        0.35           ?
0.54        0.26           ?
0.49        0.51           ?


my first question is how the classifiers (e.f., naive bayes or decision...) construct the confusion matrix? do they use 50% as the cut-point to build the confusion matrix (in binary classes), or no they use a specific function to calculate the optimal threshold? My second question is, can we use the AUC function to calculate the optimal threshold and use it to build the confusion matrix for all classifiers?