- 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)
P(cold v rainy) = 0.01 + 0.10 + 0.04 + 0.20 + 0.05 = 0.40
P(cold|rainy) = 0.10 / 0.15 = 0.666
- 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?
P(rich|hardworking) = 0.6
P(hardworking) = 0.5
P(rich|richparents) = 0.9
P(richparents) = 0.2
P(hardworking|rich) P(rich|hardworking) * P(hardworking) 0.6 * 0.5
------------------- = ------------------------------------ = --------- = 1.666
P(richparents|rich) P(rich|richparents) * P(richparents) 0.9 * 0.2
- 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?
P(~J|B & E) = 1 - P(J|B & E)
= 1 - ( P(J|A) * P(A|B & E) + P(J|~A) * P(~A|B & E) )
= 1 - ( 0.90 * 0.95 + 0.05 * 0.05 )
= 1 - ( 0.855 + 0.0025 )
= 1 - 0.8575
= 0.1425