I want to calculate P(L) for the given Bayesian Network. The solution that I am presented with by the lecturer is 0.170
My calculation path is as following. Since we know that in a Bayesian network the probability distribution of a random variable depends on evidence given through its parents
P(L) = P(L | Parent (L))
P(R=t) = 0.1 R(R=f) = 1 - P(R=t) = 0.9
P(T=t|R=t) = 0.8 P(T=t|R=f) = 0.1
P(L=t|T=t) = 0.3 P(L=t|T=f) = 0.1
P(T=t) = P(R=t) * P(T=t|R=t) + P(R=f) * P(T=t|R=f) = 0.1 * 0.8 + 0.9 * 0.1 = 0.17
P(T=f) = 1 - P(T=t) = 1 - 0.17 = 0.83
P(L) = P(T=t) * P(L=t|T=t) + P(T=f) * P(L=t|T=f) = 0.17 * 0.3 + 0.1 * 0.83 = 0.134
Sadly my result is 0.134 and not 0.17. I am a bit confused since P(T) seems to be 0.170 but I was asked about P(L)
Your calculations check out okay.$$\mathsf P(L=t)=0.134$$