The above diagram is the Bayesian Network. I want to find P(M=t|A=t && E=f)
I have followed the follwoing steps. P(M=t|A=t && E=f) = P(M=t && A=t && E=f)/ P(A=t && E=f)
P(M=t && A=t && E=f)= P(M=t|A=t) *P(A=t|E=f && B=t) *P(E=f) *P(B=t)+ P(M=t|A=t) *P(A=t|E=f && B=f) *P(E=f) *P(B=f)
Now to calculate P(A=t && E=f),
I have followed-
P(A=t && E=f)= P(A=t|E=f)*P(E=f)
Now to calculate P(A=t|E=f),
P(A=t|E=f)=P(A=t|E=f && B=t)*P(B=t)+ P(A=t|E=f && B=f)*P(B=f)
Am I correct? Any kind of help would be appreciated.
Thanks.
Note that $M$ and $E$ are conditionally independent given A. Thus, the probability you are looking for is already given in your diagram:
$$P(M=t|A=t \wedge E=f)\,\,=\,\,P(M=t|A=t)$$