# Calculate probability in graphical model

I have the following graphical model, in which I wish to compute $$p(Intelligence = 1|Letter = 1, SAT = 1)$$

But I'm not sure how to rewrite $$p(Intelligence = 1|Letter = 1, SAT = 1)$$? I was told to consider the formula $$p(D,I,G,L,S)=p(D)p(I)p(G|D,I)p(S|I)p(L|G)$$ (which applies to this model), but I don't see how someone can get something with $$p(I|L,S)$$? Is it correct to assume $$p(I|L,S)=\frac{p(I,L,S)}{p(L,S)}$$?

• LRS25, as part of the question, I think you'll need to write out how you used Bayes theorem. B.T. is clearly going to be required, so the question is how. To help, people will need to see where you might have gotten stuck. One thing that might help you figure out the answer yourself is to work first on easier questions. The answers to them will either be part of the answer to your full question, or they will be examples that will help you see how to answer the full question. For example, how can you calculate $p(I=1|G = 1)$? If you can answer that, it will probably help you see what's next. – Mars Feb 24 at 6:47
• My problem is that I dont know how to rewrite $𝑝(𝐼𝑛𝑡𝑒𝑙𝑙𝑖𝑔𝑒𝑛𝑐𝑒=1|𝐿𝑒𝑡𝑡𝑒𝑟=1,𝑆𝐴𝑇=1)$ correctly, so I dont really know what to calculate. – LRS25 Feb 24 at 19:26
• Is it correct that $p(I|L,S)=\frac{p(I,L,S)}{p(L,S)}$? – LRS25 Feb 24 at 20:26
• Yes, that's almost always a good way to define conditional probability, and I'm sure that you can assume that it's a correct definition in the context of the exercise you're working on. You're going to have to go through a bunch of steps to infer the value of $p(I|L,S)$, so I recommend working on individual steps, first. Start with $p(I|G)$. – Mars Feb 25 at 2:49