+sahdeV ok I got it... Observation we have is +u and not -u. So there are 4 ways in which +u is possible. Rain, Rain, Umbrella or TT-U Sun Rain Umbrella or FT-U Sun Sun Umbrella or FF-U Rain Sun Umbrella or TF-U Probability of each is respectively: 0.5*0.7*0.9 0.5*0.3*0.9 0.5*0.7*0.2 0.5*0.3*0.2 T-U probability is therefore 63+27/(63+27+14+6)=0.818 F-U probability is 14+6/(63+27+14+6)-0.182 *************** For the next stage, time based update alone gives us probabilities as B'(T)=0.818*0.7+0.182*0.3=0.6272 B'(F)=0.818*0.3+0.182*0.7=0.3728 observation (u+) based updates give us B(T)=0.6272*0.9/(0.6272*0.9+0.3728*0.2)=0.883 B(F)=0.3728*0.2/(0.6272*0.9+0.3728*0.2)=0.117

@@vedhasp Thank you very much.