Machine-learning algorithm / library for outcome prediction
It is a basic classification model. Our focus is to train the model using training dataset and evaluate its performance with the test set.

In your case, assume you have 10 numbers as input and a binary output.
Consider random 8 entries as your training data and train it with any classification algorithm using R/Python. Then test it on the remaining entries which acts as a test data.

Since it is associated with classification we need to consider performance metrics like accuracy, precision and recall based on the labeled feature.

For more details on classification try here