# An Example of Probabilistic Reasoning

```An Example of Probabilistic Reasoning
A probabilistic classifier consists of a probabilistic rule base, an inference engine
and a classification system. The probabilistic classifier is able to detect if the detected
bio-gene is True (T) or False (F).
Probabilit
y
F
1.0
Probabilit
y
“Green”
Overlap T
“Red”
1.0
Bio-gene
Belief
Degree
Bio-Value
50
0

100
0
0.4
0.75 1.0
Probabilistic Rule Base
Rule 1: If atomic number is in F region, Then &quot;Green&quot;;
Rule 2: If atomic number is in T region, Then &quot;Red&quot;.

Probabilistic Reasoning
Assume biological value (Bio-V) = 50, then probabilistic inference gives
BioWeapon-Belief Degree = GC(Re d ) P(T Bio  V  50)  GC(Green) P( F Bio  V  50) ,
where GC (Re d ) and GC (Green) are the centers of gravity of the triangles for
Alarm and No-Alarm. Then GC(Re d )  2 * (1.0  0.4) / 3  0.4  0.8 ,
and GC(Green)  0.75 / 3  0.25 . Now we suppose P(T Bio V  50)  0.3 ,
P( F Bio V  50)  0.6 , then Belief Degree = 0.25  0.6  0.8  0.3  0.39 .
 Classification
Finally, the classification module selects “Check” (i.e., “Green”) because Belief
Degree is less than 75% (If larger than 75%, then No-Check).
```