Basis of Binary Classification Probability I am fairly new to Machine Learning and recently I have built a binary classification model and the model architecture is an MLP with two hidden layers. I am predicting, from a protein sequence, the probability of a residue being mutated ("1") or not ("0"). I had a query regarding the output that we receive after the model predicts the binary classified output.
I can receive the output in two forms from a binary classifier. One is the binary class i.e. "0" or "1" and another is the probability of a residue being a "0" or "1". I wanted to know on what basis the probability is being calculated. For eg, suppose there are 100 students and 4 students pass the exam. Then the probability of passing the exam becomes 4/100 or 0.04. We say that "out of 100 students" 4 passes the exam. Now I have a sequence of amino acids where the total length of the sequence is 700 and my model gives me the probability of each residue being mutated ("1") or not ("0"). Now I get a probability of 0.356 for a particular residue, say at position 10. Now I know that the residue at position 10 has a probability of 0.356 suggesting that it has a 35.6% chance of being mutated. But can I say that "out of 700 residues", the residue at position 10 has a probability of being mutated? Because then the probability will become 1/700 which is less than 0.356.
I get the understanding that the binary classification will have a Bernoulli distribution and every position will have a specific value. My concern is on what basis the probability is being calculated? How does the model calculate the probability of a particular value, say there are total of 100 values?

The MLP model outputs the probability as the sum of invidual features gains for each prediction.
I had a similiar problem and the best way to ensure the gains as a real probability is plotting the outputs distribution for the test set, you can also transform the outputs using scalers to represent a know probability distribution.
