Yes, this seems like a classification problem. So if you want to see if a single subject belongs to one of two groups and you have a bunch of other subjects where you know which group they are in (labels), you can just 'score' the single subject.
The simplest thing would be to create a logistic regression model with outcome variable A or B and use the model coefficient to get a probability of the single subject being in either group. Though, you don't have to use logistic regression since all you want is a probability. So you could probably also use support vector machines, random forest, gradient boosted trees, or perhaps neural networks -> any classifier.