Pr(Acc)=[0.2 0.8]

Pr(Trav)=[0.95 0.05]

Pr(Fraud|Trav)=[[0.996 0.004]
 [0.99  0.01 ]]

Pr(FP|Fraud,Trav)=[[[0.99 0.01]
  [0.9  0.1 ]]

 [[0.1  0.9 ]
  [0.1  0.9 ]]]

Pr(OP|Acc,Fraud)=[[[0.9 0.1]
  [0.7 0.3]]

 [[0.4 0.6]
  [0.2 0.8]]]

Pr(PT|Acc)=[[0.99 0.01]
 [0.9  0.1 ]]

2b) Pr(Fraud)

Restricting factors

f0(['Acc'])=[0.2 0.8]

f1(['Trav'])=[0.95 0.05]

f2(['Trav' 'Fraud'])=[[0.996 0.004]
 [0.99  0.01 ]]

f3(['Trav' 'Fraud' 'FP'])=[[[0.99 0.01]
  [0.9  0.1 ]]

 [[0.1  0.9 ]
  [0.1  0.9 ]]]

f4(['Acc' 'Fraud' 'OP'])=[[[0.9 0.1]
  [0.7 0.3]]

 [[0.4 0.6]
  [0.2 0.8]]]

f5(['Acc' 'PT'])=[[0.99 0.01]
 [0.9  0.1 ]]

Eliminating hidden variables

Eliminating Trav
New factor: f6(['Fraud' 'FP'])=[[9.41688e-01 5.40120e-02]
 [3.47000e-03 8.30000e-04]]

Eliminating FP
New factor: f7(['Fraud'])=[0.9957 0.0043]

Eliminating OP
New factor: f8(['Acc' 'Fraud'])=[[1. 1.]
 [1. 1.]]

Eliminating Acc
New factor: f9(['Fraud' 'PT'])=[[0.918 0.082]
 [0.918 0.082]]

Eliminating PT
New factor: f10(['Fraud'])=[1. 1.]

Multiplying remaining factors
Unnormalized answer: f11(['Fraud'])=[0.9957 0.0043]

Normalizing the answer
Normalized answer: f12(['Fraud'])=[0.9957 0.0043]

Pr(Fraud)=[0.9957 0.0043]

2b) Pr(Fraud|FP,~OP,PT)

Restricting factors

f0(['Acc'])=[0.2 0.8]

f1(['Trav'])=[0.95 0.05]

f2(['Trav' 'Fraud'])=[[0.996 0.004]
 [0.99  0.01 ]]

f3(['Trav' 'Fraud'])=[[0.01 0.1 ]
 [0.9  0.9 ]]

f4(['Acc' 'Fraud'])=[[0.9 0.7]
 [0.4 0.2]]

f5(['Acc'])=[0.01 0.1 ]

Eliminating hidden variables

Eliminating Trav
New factor: f6(['Fraud'])=[0.054012 0.00083 ]

Eliminating Acc
New factor: f7(['Fraud'])=[0.0338 0.0174]

Multiplying remaining factors
Unnormalized answer: f8(['Fraud'])=[1.8256056e-03 1.4442000e-05]

Normalizing the answer
Normalized answer: f9(['Fraud'])=[0.99215129 0.00784871]

Pr(Fraud|FP,~OP,PT)=[0.99215129 0.00784871]

2c) Pr(Fraud|FP,~OP,PT,Trav))

Restricting factors

f0(['Acc'])=[0.2 0.8]

f1([])=0.05

f2(['Fraud'])=[0.99 0.01]

f3(['Fraud'])=[0.9 0.9]

f4(['Acc' 'Fraud'])=[[0.9 0.7]
 [0.4 0.2]]

f5(['Acc'])=[0.01 0.1 ]

Eliminating hidden variables

Eliminating Acc
New factor: f6(['Fraud'])=[0.0338 0.0174]

Multiplying remaining factors
Unnormalized answer: f7(['Fraud'])=[0.0495 0.0005]

Unnormalized answer: f7(['Fraud'])=[0.04455 0.00045]

Unnormalized answer: f7(['Fraud'])=[1.50579e-03 7.83000e-06]

Normalizing the answer
Normalized answer: f8(['Fraud'])=[0.99482697 0.00517303]

Pr(Fraud|FP,~OP,PT,Trav)=[0.99482697 0.00517303]

2d) Pr(Fraud|OP)

Restricting factors

f0(['Acc'])=[0.2 0.8]

f1(['Trav'])=[0.95 0.05]

f2(['Trav' 'Fraud'])=[[0.996 0.004]
 [0.99  0.01 ]]

f3(['Trav' 'Fraud' 'FP'])=[[[0.99 0.01]
  [0.9  0.1 ]]

 [[0.1  0.9 ]
  [0.1  0.9 ]]]

f4(['Acc' 'Fraud'])=[[0.1 0.3]
 [0.6 0.8]]

f5(['Acc' 'PT'])=[[0.99 0.01]
 [0.9  0.1 ]]

Eliminating hidden variables

Eliminating Trav
New factor: f6(['Fraud' 'FP'])=[[9.41688e-01 5.40120e-02]
 [3.47000e-03 8.30000e-04]]

Eliminating FP
New factor: f7(['Fraud'])=[0.9957 0.0043]

Eliminating Acc
New factor: f8(['Fraud' 'PT'])=[[0.4518 0.0482]
 [0.6354 0.0646]]

Eliminating PT
New factor: f9(['Fraud'])=[0.5 0.7]

Multiplying remaining factors
Unnormalized answer: f10(['Fraud'])=[0.49785 0.00301]

Normalizing the answer
Normalized answer: f11(['Fraud'])=[0.99399034 0.00600966]

Pr(Fraud|OP)=[0.99399034 0.00600966]

2d) Pr(Fraud|OP,PT)

Restricting factors

f0(['Acc'])=[0.2 0.8]

f1(['Trav'])=[0.95 0.05]

f2(['Trav' 'Fraud'])=[[0.996 0.004]
 [0.99  0.01 ]]

f3(['Trav' 'Fraud' 'FP'])=[[[0.99 0.01]
  [0.9  0.1 ]]

 [[0.1  0.9 ]
  [0.1  0.9 ]]]

f4(['Acc' 'Fraud'])=[[0.1 0.3]
 [0.6 0.8]]

f5(['Acc'])=[0.01 0.1 ]

Eliminating hidden variables

Eliminating Trav
New factor: f6(['Fraud' 'FP'])=[[9.41688e-01 5.40120e-02]
 [3.47000e-03 8.30000e-04]]

Eliminating FP
New factor: f7(['Fraud'])=[0.9957 0.0043]

Eliminating Acc
New factor: f8(['Fraud'])=[0.0482 0.0646]

Multiplying remaining factors
Unnormalized answer: f9(['Fraud'])=[0.04799274 0.00027778]

Normalizing the answer
Normalized answer: f10(['Fraud'])=[0.99424535 0.00575465]

Pr(Fraud|OP,PT)=[0.99424535 0.00575465]