enter image description here

I am working through a text book (Probabilistic Graphical Models, Principles and Techniques) to learn BNs, but I am confused as to the accuracy of the example. The text references the figure above. We are told that;

P(l^1) ~ 0.502

Using the tilde instead of equals sign when numbers are given is the source of confusion. If I average the l^1 column, I get 0.5033, which should not by any means round down to 0.502. So, is the answer really 0.503 or am I over simplifying the solution?

Next, the text explains that P(l^1 | i^0) ~ 0.389. Though, I am far from getting anything close to that value given the numbers inthe image. Could someone show me the correct calculations to get 0.389?

I am trying to realize whether I am especially challenged in statistics, or if the text is not explained in the best manner for me to learn.

Just to be complete, here is the example copied from the text;

enter image description here

  • 2
    $\begingroup$ Which textbook are you using? It might help to have a reference. $\endgroup$
    – Maurits M
    Jul 10, 2019 at 19:29

1 Answer 1


The text is trying to illustrate how the operations of conditioning and marginalization work in a Bayesian network.

You should not be computing $P(l^1)$ by averaging the $l^1$ column. Instead, you should write the joint distribution over $D$, $I$, $G$, and $L$ as a product of CPD factors using the chain rule for Bayesian networks. Then you should marginalize out $D$, $I$, and $G$ by summing the joint distribution over all possible assignments to these random variables. The result will be the marginal distribution over $L$, i.e. two numbers specifying $P(l^0)$ and $P(l^1)$.

To compute the conditional probability $P(l^1 | i^0)$, set $P(i^0) = 1$ and ignore the rows in the grade distribution where $I = i^1$, then follow the same procedure as above.

Chapter 2 in the textbook you mentioned reviews the relevant concepts in basic probability.

  • $\begingroup$ Bless my heart for trying. Can you suggest a decent textbook that covers the relevant concepts more thoroughly? $\endgroup$
    – jsfa11
    Jul 10, 2019 at 22:25
  • $\begingroup$ I've heard good things about Introduction to Probability by Bertsekas. $\endgroup$
    – tddevlin
    Jul 10, 2019 at 22:46
  • 1
    $\begingroup$ For the record, I bought and found Introduction to Probability by Bertsekas to be the best probability book I have read so far. Thanks for that suggestion. $\endgroup$
    – jsfa11
    Jan 21, 2020 at 2:13

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