I have got the following Network and porbabilites enter image description here

And I need to Calculate the probability $P(C=False)$

I triend using the formula for joint porability distributions $P(X_1,…,X_n)= \prod_{i=1}^{n}P(X_i∣ parents (X_i))$
,and got $P(C=False)=P(C=False|A,B)$.

If I am not wrong, you can infer that $P(C=False|A,B) = 0.75$ from the table of probabilites , but I would like to know what is the general way to solving a problem like this in case not all the probabilities for each case are the same.


1 Answer 1


This is the way to calculate:

$$\begin{align} P(C=False)&=\sum_{a,b} P(C=False,A=a,B=b)\\ &=\sum_{a,b}P(C=False|A=a,B=b)P(A=a, B=b)\\ &=\sum_{a,b}P(C=False|A=a,B=b)P(A=a)P(B=b) \end{align}$$

Here, $a, b$ can be $True, False$. Values in the summation can be substituted from the table.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.