Predicting the probability of the occurence of an event

For a research project that I am working on, I need to predict the probability of the occurrence of a certain event.

To be more precise, I need to predict the probability of a student submitting any solution to a certain assignment (Y) or not (N).

The only thing that I have to help me is data from previous years in this form:

Student 1 – Y Y Y Y N Y Y Y
Student 2 – N N N Y Y Y Y N
…


Each line represents one student and the columns represent the ordered list of assignments (Y- the student has submitted at leat one solution for that assignment), (N – the student hasn’t submitted any solution for that assignment)

Given a certain sequence of events, I need to calculate the probability of the next event. For instance:

If in the first three assignments the student had one of the following behavior, what will happen for assignment number 4?

Y N Y ?
N N N ?
Y Y Y ?
…


I’ve already calculated the probabilities based on the overall occurrence of a Y or N for a given assignment. I’ve also calculated the probability of the occurrence of a Y after an N, and a Y after a Y, and so on… I’ve also developed a method to determine the probability using a Markov Chain... However, I am not sure which method is the most "scientifically fitted" for this kind of problem…

Any suggestions will be very welcome.

Tks.

Nuno.

• Out of curiosity, what method did you develop for using the Markov Chain? – EhsanF Aug 3 '16 at 12:48