  The probability of an event is in the range of [0, 1]. In a sample space S,
the value of probability determines whether an outcome is true or false. The
probability of an event Pr(A) that will never occur = 0. The probability of the
event Pr(B) that will certainly occur = 1. This makes both events A and B thus
a certainty. Furthermore, the sum of probabilities Pr(E1) + Pr(E2) + ... +
Pr(En) of a finite set of events in a given sample space S = 1. Conversely, the
difference of the sum of two probabilities that will certainly occur is 0.
Firstly, this paper discusses Bayes' theorem, then complement of probability
and the difference of probability for occurrences of learning-events, before
applying these in the prediction of learning objects in student learning. Given
the sum total of 1; to make recommendation for student learning, this paper
submits that the difference of argMaxPr(S) and probability of
student-performance quantifies the weight of learning objects for students.
Using a dataset of skill-set, the computational procedure demonstrates: i) the
probability of skill-set events that has occurred that would lead to higher
level learning; ii) the probability of the events that has not occurred that
requires subject-matter relearning; iii) accuracy of decision tree in the
prediction of student performance into class labels; and iv) information
entropy about skill-set data and its implication on student cognitive
performance and recommendation of learning [1].

Artificial Intelligence;Computers and Society