## Artificial Intelligence: Problem Set 5

Assigned: Oct. 24

Due: Oct. 31

Consider the Bayesian network shown below:

In this network, B is independent of A absolutely; D is independent of A and
B given C; and E is independent of A, B, and D given C.
Assume that all the random variables are Boolean and that
the following probabilities are recorded for the network:

Prob(A=T) = 0.9

Prob(B=T) = 0.5

Prob(C=T | A=T,B=T) = 0.8

Prob(C=T | A=T,B=F) = 0.7

Prob(C=T | A=F,B=T) = 0.7

Prob(C=T | A=F,B=F) = 0.0

Prob(D=T | C=T) = 0.8

Prob(D=T | C=F) = 0.5

Prob(E=T | C=T) = 0.2

Prob(E=T | C=F) = 0.9

Compute the following quantities:
- Prob(B=F | A=T).
- Prob(C=T).
- Prob(B=T | C=T)
- Prob(D=T)
- Prob(E=T | B=T,C=T).
- Prob(E=T | B=T).
- Prob(C=F | E=T).