1
2
3
4
5
6
7
8
9
10
11
12
ABCDEFGH
Purchase Price $3
Selling Price $8
Payoff Table
Sell Sell Sell Sell Expected
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
ABCDEFGH
Purchase Price $3
Selling Price $8
Payoff Table
Sell Sell Sell Sell Expected
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
ABCDEFGH
Purchase Price $3
Selling Price $8
Payoff Table
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
ABCDEFGH
Purchase Price $3
Selling Price $8
Payoff Table
Sell Sell Sell Sell Expected
Alternative 10 11 12 13 Payoff
State of Nature
1
2
3
4
5
6
7
8
ABCDEF
Payoff Table ($million) Expected
Alternative State of Nature (Economy) Payoff
(Investment) Improving Stable Worsening ($million)
Conservative 30 5 -10 1.5
1
2
3
4
5
6
7
8
ABCDEF
Payoff Table ($million) Expected
Alternative State of Nature (Economy) Payoff
(Investment) Improving Stable Worsening ($million)
1
2
3
4
5
6
7
8
ABCDEF
Payoff Table ($million) Expected
Alternative State of Nature (Economy) Payoff
(Investment) Improving Stable Worsening ($million)
Conservative 30 5 -10 4.5
0.1
Improving
30
30 30
0.7
Conservative Stable
210
5051010
0.2
Worsening
-30
-30 -30
0.1
Improving
15 15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
ABC D E FG H I JK
0.1
Improving
0.1
Improving
40
40 40
0.5
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
ABC D E FG H I JK
0.1
Improving
30
30 30
0.3
8 0 -11 10 10
0.6
Worsening
-30
-30 -30
0.1
Improving
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
ABC D E FG H I JK
0.1
Improving
40
40 40
0.7
Speculative Stable
210
5051010
0.2
Worsening
15
15 15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
ABC D E FG H I JK
0.1
Improving
30
30 30
0.1
Improving
-10
-10 -10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
ABCDEFG
Probability
of Stable Expected Payoff ($million)
Economy Conservative Speculative Countercyclical
-25
-20
-15
-10
0
5
10
15
Probability of Stable Economy
1
2
3
4
7
8
ABCDE
Payoff Table ($thousand) Expected
Payoff
Alternative S1S2($thousand)
A180 25 47
State of Nature
0.4
State 1
80
1
2
3
8
9
25
10
11
12
13
14
30
15
16
17
18
19
20
21
22
23
24
60
25
26
27
28
29
ABC D E FG H I JK
0.2
State 1
80
25
30
2
46
0
46
0.8
State 2
50
50
50
0.2
60
1
2
3
8
9
25
10
11
12
13
14
30
15
16
17
18
19
20
21
22
23
24
60
25
26
27
28
29
ABC D E FG H I JK
0.6
State 1
80
25
30
1
58
0
38
0.4
State 2
50
50
50
0.6
60
1
3
8
9
25
10
11
12
13
14
30
15
16
46
46
17
18
20
21
22
23
24
60
25
26
27
28
29
ABC D E FG H I JK
0.2
80
25
0.2
State 1
30
2
50
60
1
2
3
4
6
7
ABCDEF
Payoff Table ($thousand) Expected
State of Nature Payoff
Alternative S1S2S3($thousand)
A1220 170 110 194
0.6
State 1
220
220
220
170
194
170
110
110
1
194
200
200
180
189
180
0.1
State 3
150
150
150
1
2
3
4
7
8
9
194
170
10
11
12
13
14
110
15
16
194
17
18
19
20
21
22
23
24
189
180
25
26
27
28
29
150
ABC D E FG H I JK
0.6
State 1
220
220 220
170
110
1
State 1
200
200
200
0.3
180
150
1
2
3
4
5
6
7
8
9
194
170
10
11
12
13
14
110
15
16
17
18
19
20
21
22
23
24
189
180
25
26
27
28
29
150
ABC D E FG H I JK
0.6
State 1
220
220 220
0.3
170
110
1
194
0.6
State 1
200
200
200
180
150
1
2
3
4
5
7
8
9
194
170
10
11
12
13
14
110
15
16
17
18
19
20
21
22
23
24
189
180
25
26
27
28
29
150
ABC D E FG H I JK
0.6
State 1
220
220 220
170
110
1
194
0.6
State 1
200
200
200
180
150
0.3
Dry
20
20 20
0.3
Dry
22.5
22.5 22.5
31.5 0.3
Dry
30
30 30
0.3
Dry
20
1
2
3
4
5
6
7
8
9
ABCDEF
Payoff Table ($thousand) Expected
State of Nature (Weather) Payoff
Alternative Dry Moderate Damp ($thousand)
1
2
3
4
5
6
7
8
9
ABCDEF
Payoff Table ($thousand) Expected
State of Nature (Weather) Payoff
Alternative Dry Moderate Damp ($thousand)
1
2
3
4
5
6
7
8
9
ABCDEF
Payoff Table ($thousand) Expected
State of Nature (Weather) Payoff
Alternative Dry Moderate Damp ($thousand)
Crop 1 20 35 40 32
1
2
3
4
5
6
7
8
9
ABCDEF
Payoff Table ($thousand) Expected
State of Nature (Weather) Payoff
Alternative Dry Moderate Damp ($thousand)
1
2
3
4
5
6
9
10
ABCDEF
x = 50
Payoff Table ($hundred) Expected
State of Nature Payoff
Alternative S1S2S3($hundred)
A1100 50 10 54
1
2
3
4
5
6
9
10
ABCDEF
x = 75
Payoff Table ($hundred) Expected
State of Nature Payoff
Alternative S1S2S3($hundred)
A1150 50 10 74
1
2
3
4
7
8
ABCDEF
Payoff Table ($thousands) Expected
State of Nature Payoff
Alternative S1S2S3($thousands)
A1400 0.8
Alternative 1
4
44
0.3
State 3 Alternative 2
30
01 00
Alternative 3
1
11
1
2
3
6
7
ABCDEF
Payoff Table State of Nature Expected
Alternative S1S2S3Payoff
A1$50 $100 -$100 $35
Alternative 1
50
50 50
0.5
State 1 Alternative 2
10
050 0 0
Alternative 3
40
40 40
Alternative 1
-100
-100 -100
1
2
3
4
7
8
ABCDEF
Payoff Table ($thousands) Expected
State of Nature Payoff
Alternative S1S2S3($thousands)
A1-100 10 100 33
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E F G H
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability FSS USS
Oil 0.25 0.8 0.2
Finding P(Finding) Oil Dry
FSS 0.5 0.4 0.6
USS 0.5 0.1 0.9
P(Finding | State)
Finding
0.1
Oil
670
Drill 800 670
-100 -50 0.9
0.5 Dry
Unfavorable -130
2 0 -130
060
1 Sell
125 60
90 60
0.25
Oil
700
Drill 800 700
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
ABCD EFG H I JKL M NO P QRS
Decision Tree for Goferbroke Co. Problem (With Survey)
0.1
Oil
670
Drill 800 670
-100 190 0.6
0.5 Dry
Favorable -130
1 0 -130
0 190
Input Output
P(FSS|Oil) Expected Payoff
0 127
0.05 119.375
0.1 111.75
0.15 104.125
0.2 100
0.25 100
0.35 100
0.4 100
0.45 100
0.5 100
0.55 100
0.6 100
0.65 102.125
0.7 109.75
0.75 117.375
0.8 125
0.85 132.625
0.9 140.25
0.95 147.875
1 155.5
100
110
130
140
150
160
Expected
Payoff
Sensit
Input Output
P(FSS|Dry) Expected Payoff
0 182
0.05 174.875
0.1 167.75
0.15 160.625
0.2 153.5
0.55 103.625
0.6 100
0.65 100
0.7 100
0.75 100
0.8 100
0.85 100
0.9 100
0.95 100
1 100
150
160
170
180
190
Expected
Sensit
1
Input Variables Values
90% 92% 94% 96% 98% 100%
Cost of Survey 27 27.6 28.2 28.8 29.4 30
Output Variable Values (Expected Payoff)
90% 92% 94% 96% 98% 100%
Output Variable Percent (Expected Payoff)
90% 92% 94% 96% 98% 100%
102% 104% 106% 108% 110%
102% 104% 106% 108% 110%
102% 104% 106% 108% 110%
84%
88%
92%
% Change in Expected Payoff
Input Values Output Values (Expected Payoff) Percent
Input Variable Low Base High Low Base High Swing Variance
Revenue if Oil 600 800 1000 90 125 165 75 83.7%
600
1000
Revenue if Oil
Sensit – Sensitivity Analysis – Tornado
1
2
3
4
5
6
7
ABCDEF
Payoff Table ($thousands) Expected
State of Nature (Credit Record) Payoff
Alternative Poor Average Good ($thousands)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E F G H
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Poor Average Good
Poor 0.2 0.5 0.4 0.1
Finding P(Finding) Poor Average Good
Poor 0.360 0.278 0.556 0.167
Average 0.450 0.178 0.556 0.267
Good 0.190 0.105 0.263 0.632
P(Finding | State)
Finding
0.278
Poor
-15000 -20000
0.178
Poor
-15000 -20000
0.105
Poor
-15000 -20000
0.263
Extend Credit Average
0 8695 10000 5000
0.19 0.632
Good Good
21
8000 0 8695 20000 15000
-20000
5000
15000
-5000
-20000
5000
15000
-5000
1
2
5
6
ABCDE
Payoff Table Expected
Alternative S1S2Payoff
State of Nature
Alternative 1
0.4 400
State 1 400 400
1
0 100
Alternative 2
100
100 100
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E F G H
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Predict S1 Predict S2
Finding P(Finding) Actual S1 Actual S2
Predict S1 0.36 0.667 0.333
Predict S2 0.64 0.250 0.750
P(Finding | State)
Finding
1
2
5
6
ABCDE
Payoff Table Expected
Alternative S1S2Payoff
State of Nature
1
2
5
6
ABCDE
Payoff Table Expected
Alternative S1S2Payoff
State of Nature
0.667
S1 occurs
300
Choose A1 400 300
0 -75 0.75
S2 occurs
0.64 -200
Presdict S2 -100 -200
2
0 -25 0.25
S1 occurs
-100
Choose A2 0 -100
2
100 0 -25 0.75
S2 occurs
0
100 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E F G H
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Positive Negative
Finding P(Finding) User Nonuser
Positive 0.14 0.679 0.321
Negative 0.86 0.006 0.994
P(Finding | State)
Finding
1
2
3
4
5
6
7
ABCDE
Payoff Table ($millions) Expected
Payoff
Alternative Successful Unsuccessful ($millions)
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Predict Successful Predict Unsuccessful
Finding P(Finding) Successful Unsuccessful
Predict Successful 0.633 0.842 0.158
Predict Unsuccessful 0.367 0.364 0.636
P(Finding | State)
Finding
0.842
Successful
1.4
Develop Product 1.5 1.4
1 Don’t Develop
0.52 -0.1
0 -0.1
0.6667
Successful
1.5
Develop Product 1.5 1.5
Input Variables Values
75% 80% 85% 90% 95%
Output Variable Values (Expected Payoff)
75% 80% 85% 90% 95%
Output Variable Percent (Expected Payoff)
75% 80% 85% 90% 95%
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Expected
Payoff
Value
100% 105% 110% 115% 120% 125%
100% 105% 110% 115% 120% 125%
100% 105% 110% 115% 120% 125%
Input Values Output Values (Expected Payoff)
Input Variable Low Base High Low Base High Swing
1.125
1.35
0.075
1
2.25
0.125
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7
Profit if Success
Loss if Unsuccessful
Cost of Survey
Expected Payoff
Percent
Variance
1
2
3
4
5
ABCDE
Payoff Table Expected
Alternative p = 0.05 p = 0.25 Payoff
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Defective Nondefective
Finding P(Finding) p = 0.05 p = 0.25
Defective 0.09 0.444 0.556
Nondefective 0.91 0.835 0.165
P(Finding | State)
Finding
0.444
p=0.05
Screen -1500 -1625
-125 -1392.95 0.835
p=0.05
Screen -1500 -1625
0.8
p=0.05
Screen -1500 -1500
Don’t Pre-screen -1500 -1500
2
0 -1350 0.8
p=0.05
Don’t screen -750 -750
-1625
-1625
-875
-3875
-750
-3750
Input Output
Prior Probability of Selling 10,000 Expected Payoff
054
0.05 51.3
0.1 48.6
0.15 45.9
0.2 43.2
0.25 40.5
0.3 37.8
0.35 35.1
0.4 32.4
15
20
25
30
35
40
45
50
55
Expected
Payoff
Sensit –
Sensitivity A
0.5 0.6 0.7 0.8 0.9 1
bility of Selling 10,000
Analysis
-Plot
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Predict Sell 10,000 Predict Sell 100,000
Finding P(Finding) Sell 10,000 Sell 100,000
Predict Sell 10,000 0.5 0.667 0.333
Predict Sell 100,000
0.5 0.333 0.667
P(Finding | State)
Finding
0.667
Sell 10,000
-1
Build computers 6 -1
-6 35 0.667
0.5 Sell 100,000
Predict sell 100,000 53
16053
035
2 Sell rights
27 14
15 14
15 15
0.667
Sell 10,000
-1
Build computers 6 -1
0.333
-1 26 Sell 10,000
-1
Build computers 6 -1
-6 35 0.667
0.5 Sell 100,000
Predict sell 100,000 53
16053
035
Input Output
Sell Rights Payoff Expected Payoff
13.5 27.0
14 27.0
15 27.0
15.5 27.0
16 27.0
16.5 27.0
0.0
5.0
10.0
15.0
25.0
30.0
Expected
Payoff
5
16 16.5
Input Output
Assembly Line Cost Expected Payoff
5.4 27.6
5.5 27.5
5.6 27.4
5.7 27.3
5.8 27.2
5.9 27.1
6 27.0
6.1 26.9
6.2 26.8
6.5 26.5
6.6 26.4
26.0
26.5
27.0
27.5
28.0
Expected
Payoff
Sensit – Sensitivity Analysis – Plot
2
6.3 6.4 6.5 6.6
Input Output
Marginal Profit Expected Payoff
0.00054 23.7
0.00056 24.8
0.00058 25.9
0.0006 27.0
0.00062 28.1
0.00064 29.2
0.00066 30.3
23.0
24.0
25.0
26.0
27.0
28.0
29.0
30.0
31.0
Expected
Payoff
Sensit – Sensitivity Analysis – Plot
2
0.00064 0.00066
Input Variables Values
90% 92% 94% 96% 98%
Output Variable Values (Expected Payoff)
90% 92% 94% 96% 98%
Output Variable Percent (Expected Payoff)
90% 92% 94% 96% 98%
23.0
24.0
25.0
90% 95% 100% 105% 110%
Payoff
% Change in Input Value
100% 102% 104% 106% 108% 110%
Input Values Output Values (Expected Payoff)
Input Variable Low Base High Low Base High Swing
0.00054
5.4
13.5
0.0
6.6
16.5
23.0 24.0 25.0 26.0 27.0 28.0 29.0 30.0
Marginal Profit
Assembly Line Cost
Sell Rights Payoff
Expected Payoff
0.4
2500
2500
10
0.5 10
2 0.5
1
2
3
4
5
6
7
ABCDE
Payoff Table ($millions) Expected
Payoff
Alternative
Winning Season
Losing Season ($millions)
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D EFGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Predict W Predict L
Winning Season 0.6 0.75 0.25
Finding P(Finding) Winning Season Losing Season
Predict W 0.55 0.818 0.182
Predict L 0.45 0.333 0.667
P(Finding | State)
Finding
0.8182
Win
2.9
Hold campaign 3 2.9
Hire William
0.3333
-0.1 1.05 Win
2.9
Hold campaign 3 2.9
0 -0.4333 0.6667
0.45 Lose
Predict lose -2.1
2 -2 -2.1
0 -0.1
0.7
Growth
Stocks Y2 24 144
0 133.2 0.3
Recession
0.7
Growth -12 108
1
20 133.2 0.7
Growth
Bonds Y2 6 126
0 127.8 0.3
Recession
12 132
4.5 94.5
0.7
Bonds Y2 Recession
099 999
0.1
1 Depression
122.94
18 108
0.7
Growth
Stocks Y2 21 126
5.5 115.5
0.7
Bonds Y2 Recession
0 121 11 121
0.1
144
108
126
132
108
126
94.5
99
55
115.5
121
132
Buy
900
900 900
0.3 0.4
Close at $9 10% Lower
2 810
0891 810 810
Buy
1100
1100 1100
0.4 0.1
Close at $11 10% Lower
1 990
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D EFGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Excellent Not Excellent
Satisfactory Box 0.9 0.8 0.2
Finding P(Finding) Satisfactory Box Unsatisfactory Box
Excellent 0.75 0.960 0.040
Not Excellent 0.25 0.720 0.280
P(Finding | State)
Finding
0.96
Satisfactory
200
Buy 200 200
1 Reject
114 0
00
0.9
Satisfactory
200
Buy 200 200
1
2
3
4
5
6
7
ABCDE
Payoff Table ($millions) Expected
Payoff
Alternative Successful Unsuccessful ($millions)
State of Nature
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Approved Not Approved
Successful 0.5 0.8 0.2
Finding P(Finding) Successful Unsuccessful
Approved 0.525 0.762 0.238
Not Approved 0.475 0.211 0.789
P(Finding | State)
Finding
0.762
Successful
38
Introduce product 40 38
0 24.905 0.238
0.525 Unsuccessful
Approved -17
1 -15 -17
Don’t introduce product
0
00
0.762
Successful
38
Introduce product 40 38
0 24.905 0.238
0.525 Unsuccessful
Approved -17
0.5
Successful
40
Introduce product 40 40
0 12.5 0.5
Unsuccessful
Don’t test -15
1 -15 -15
Input Output
Net Profit if Successful Expected Payoff
30 8.125
32 8.925
34 9.725
36 10.525
38 11.5
40 12.5
42 13.5
44 14.5
46 15.5
8
10
12
14
16
18
Expected
Payoff
Sensit – Sensitivity Analysis – Plot
44
46 48 50
Input Output
Net Loss if Unsuccessful Expected Payoff
11.25 14.375
11.75 14.125
12.25 13.875
12.75 13.625
13.75 13.125
14.25 12.875
14.75 12.625
15.25 12.375
16.75 11.90625
17.25 11.84375
17.75 11.78125
18.25 11.71875
18.75 11.65625
11.5
12
12.5
13.5
14
14.5
Sensit – Sensitivity Analysis – Plot
Input Variables Values
75% 80% 85% 90% 95%
Output Variable Percent (Expected Payoff)
75% 80% 85% 90% 95%
100% 105% 110% 115% 120% 125%
100% 105% 110% 115% 120% 125%
Input Values Output Values (Expected Payoff)
Input Variable Low Base High Low Base High
30
11.2518.75
8 9 10 11 12 13 14 15 16
Net Profit if Successful
Expected Payoff
Percent
Swing Variance
0.571
Do well in ST
14.4
Run in ST 16 14.4
0 3.26 0.429
0.4667 Do poorly in ST
Do well in NH -11.6
1 -10 -11.6
0 0.4
Don’t run in ST
0
00
Input Output
Payoff if Win ST Expected Payoff
12 0.000
13 0.000
14 0.133
15 0.400
17 0.933
18 1.200
19 1.600
20 2.000 0.0
0.5
1.5
2.0
Sensit – Sensitivity Analysis – Plot
Input Output
Loss if Lose ST Expected Payoff
7.5 1.900
8 1.600
8.5 1.300
9 1.000
10 0.667
10.5 0.567
11 0.467
11.5 0.367
0
0.5
1.5
2
Sensit – Sensitivity Analysis – Plot
Input Variables Values
75% 80% 85% 90% 95% 100%
Output Variable Percent (Expected Payoff)
75% 80% 85% 90% 95% 100%
0.0
0.5
75% 85% 95% 105% 115% 125%
% Change in Input Value
105% 110% 115% 120% 125%
Input Values Output Values (Expected Payoff) Percent
Input Variable Low Base High Low Base High Swing Variance
12
7.5
20
12.5
0.00.20.40.60.81.01.21.41.61.82.0
Payoff if Win ST
Loss if Lose ST
Expected Payoff
0.9545
Successful
1960
Hire 2000 1960
Test
0.2059
-40 1202 Successful
1960
Hire 2000 1960
0 -105 0.7941
0.34 Unsuccessful
Fail -640
2 -600 -640
0 -40
0 1220
Don’t hire
0
00
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Pass Test Fail Test
Finding P(Finding) Successful Not Successful
Pass Test 0.6600 0.9545 0.0455
Fail Test 0.3400 0.2059 0.7941
P(Finding | State)
Finding
0.143
Oil
Drill 440 440
0.5
0 78 Oil
Drill 440 440
0 120 0.5
0.3 Dry
0.25
Oil
Drill 450 450
440
-200
90
1
2
3
4
5
ABCDE
Payoff Table Expected
Alternative Earthquake No Earthquake Payoff
State of Nature
0.25
0.39347
33.015
0.4833
36
36
0.51325
100
100
1
0.86466
33.0149
12.178
0.4833
0.2162
0
0
0
0.25
State 1
0
Alternative 3 0
0
0
31.604
0.4685
49
49
25
0.5
Positive test result 0.2
1 Die
0 13 0.8
Have A 0 -2
0 6 0.8
Poor Health
Don’t treat A 10 8
0-3 0–3
0.5
Poor Health
0.5
Have A 10 9
0 19 0.5
Good Health
Treat A
30 29
7
27
-3
-2
-2
8
-1
0
10
0
10
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
AB C D E FGH
Template for Posterior Probabilities
Data:
State of Prior
Nature Probability Positive Negative
Disease A 0.5 0.8 0.2
Finding P(Finding) Disease A Disease B
Positive 0.5 0.8 0.2
Negative 0.5 0.2 0.8
P(Finding | State)
Finding
A1 $x
x1/3
3.5 -5
0.5
$141
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
ABC D E FG H I JK L M NO P QRS
Decision Tree for Goferbroke Co. Problem (With Max’s Utility Functio
0.2121
Oil
0 141.75 0.65
Dry
No Survey -105
1 -105 -105
0 141.75
Sell
90
90 90