How to calculate the probability of L from this Bayesian Network

Question

This is a follow up to a previous question posted.

I am now working on calculating P(~B|~F).

The Bayesian Network:

So far, I have:

P(~B|~F) =

P(~F|~B)(~F) / P(~B)

P(~F|~B) = P(~F, L|~B) + P(~F, ~L|~B)

(P(~F|L, ~B)*P(L|~B))+(P(~F|~L, ~B)*P(~L|~B))

0.5 * P(L) + 0.95 * P(~L)

However, I am not certain how to extract the P(L) (knowing that P(~L) = 1 - P(L)) from the graph. How can I know P(L)?

Answer 1

As requested in comments:

$$P(L=l_1)=P(L=l_1 \mid H=h_1)P(H=h_1)+P(L=l_1 \mid H=h_2)P(H=h_2)$$

so here

$$P(L=l_1) = (0.003 \times 0.2) + (0.0005 \times 0.8) = .001 \text{ and }P(L=l_2) = 1-0.001 = 0.999$$

Answer 2

$$\def\P\mathop{\,\mathsf P}\P_{\!\small B\mid F}(b_2\mid f_2)=\dfrac{\sum_{h,\ell}\P_{\!\small H}(h)\P_{\!\small L\mid H}(\ell\mid h)\P_{\!\small B\mid L}(b_2\mid\ell)\P_{\!\small F\mid B,L}(f_2\mid b_2,\ell)}{\sum_{h,\ell,b}\P_{\!\small H}(h)\P_{\!\small L\mid H}(\ell\mid h)\P_{\!\small B\mid L}(b_2\mid \ell)\P_{\!\small F\mid B,L}(f_2\mid b_2,\ell)}$$