Uncertainty

Given the joint

        sunny rainy cloudy snowing
cold     0.01  0.10   0.04    0.20
hot      0.50  0.05   0.10    0.00

what are the probabilities

P(cold v rainy)
P(cold|rainy)

If 60% of hardworking people are rich, 50% of people are hardworking, 90% of people with rich parents are rich, and 20% of people have rich parents, what is the relative likelyhood of being hardworking vs. having rich parents, given that you are rich?

Given the belief network

Burglary P(B)=0.001      Earthquake P(E)=0.002
                   \     /
                    Alarm P(A| B &  E)=0.95
                          P(A| B & ~E)=0.94
                          P(A|~B &  E)=0.29
                          P(A|~B & ~E)=0.001
                   /     \
JohnCalls P(J| A)=0.90    MaryCalls P(M| A)=0.70
          P(J|~A)=0.05              P(M|~A)=0.01

calculate (showing your calculations) the probability that John does not call given that there's been a burglary and an earthquake?