I am currently taking a free on-line AI class offered by Stanford (ai-class.com). It is the first time I am exposed to Bayes Network/Probability. I am having a little problem with the following Quiz problem:
C / \ / \ T1 T2
Given C is known and T1 and T2 are conditional independence
P(C) = 0.01
P(+ | C) = 0.9
P(- | not C) = 0.8
P(C | T1=+) = 0.043
P(T2=+ | T1=+) = ?
The solution to the problem is given below:
P(T2=+ | T1=+) = P(T2=+ | T1=+, C) * P(C | T1=+) + P(T2=+ | T1=+, not C) * P(not C | T1=+)
My question to the solution above is:
1) Why do we use total probability approach to solve the problem?
2) During the expansion, why do we add "C" and "| T1=+" to the whole equation?
The quiz question can be found here: http://www.youtube.com/watch?feature=player_embedded&v=EmLvORqH-Dg
The answer to the quiz is here: http://www.youtube.com/watch?feature=player_embedded&v=6d2lH9JP6kw
I would really appreciate it if someone can help me to understand the solution.