Bayes Net Calculation

https://dl.dropbox.com/s/746tssbnukoyw1n/Screenshot%202017-03-01%2007.56.05.png

Given Tables

P(LD=T | Cough=T) =  P(Cough=T |LD=T)  *P(LD)
                    ---------------------------
                            P(Cough)
                  =  (0.80 * 0.30 + 0.75 * 0.70) * P(LD)
                     ------------------------------------
                            P(Cough)

                  = (0.80 * 0.30 + 0.75 * 0.70) * (0.10)
                    ------------------------------------
                                P(Cough)

                  = (0.80 * 0.30 + 0.75 * 0.70) * (0.10)
                  ---------------------------------------
                  (0.80 * 0.30 * 0.10) + (0.30 * 0.30 * 0.90) + (0.75 * 0.70 * 0.10) + (0.05 * 0.70 * 0.90)

                  = 0.0765
                    -------
                    0.189

                  = 0.40476190476190477
  1. Question
\[P(LD=T|Cough=T,Fever=T)\]

// Bayesian

P(LD=T|Cough=T,Fever=T) = P(Cough=T, Fever=T | LD=T) * P(LD=T)

                        = Sum(cold) [P(Cough=T,Fever=T| LD=T,cold) * P(cold) * P(LD=T) ] // Skipped a step = that was the mistake

                        = Sum(cold) [P(Cough=T| LD=T,cold) * P(Fever=T| LD=T, cold) * P(cold) * P(LD=T) ]

                        = P(LD=T) * Sum(cold) [P(Cough=T| LD=T,cold) * P(Fever=T| cold) * P(cold)]

                        = P(LD=T) * [P(Co=T|LD=T,C=T) * P(F=T|C=T) * P(C=T) + P(Co=T|LD=T,C=F) * P(F=T|C=F) * P(C=F)]
                        = 0.10 * ((0.80 * 0.65 * 0.30) + (0.75 * 0.25 * 0.70))

                        = 0.028725

                      = P(Cough=T, Fever=T | LD=F) * P(LD=F)


                      = P(LD=F) * Sum(cold) [P(Cough=T| LD=F,cold) * P(Fever=T| cold) * P(cold)]
                      = P(LD=F) * [P(Co=T|LD=F,C=T) * P(F=T|C=T) * P(C=T) + P(Co=T|LD=F,C=F) * P(F=T|C=F) * P(C=F)]
                      = 0.90 * ((0.30 * 0.65 * 0.30) + (0.05 * 0.25 * 0.70))

                      = 0.060524999999999995

                      = 0.32184873949579834