Bayesian Networks

A Bayesian network is a probabilistic graphical model and has many applications. Here we study a simple Bayesian network.

A student has a class in the early morning. It is easy to be late to this class due to oversleeping or late bus.

Suppose that the student may oversleep ($S$) with probability 0.5, and may encounter a late bus ($B$) with probability 0.5. The events $S$ and $B$ are independent.

Given that the student is late to the class, we can infer whether the student overslept or it was the late bus.

Questions:

Please send your solution to me via email. Good luck!