I have a joint probability table of $X and Y$ with
$P(X=1)= 0.325 $
the computations for $P(Y|X=1)$ as :
$P(Y|X=1)= \frac{P(X=1,Y)}{P(X=1)}$
and for Y = 0
$P(Y=0|X=1) = 0.3846153846153846$
and for Y =1
$P(Y=1|X=1) = 0.6153846153846154$
which sum up to one, $ P(Y=0|X=1) + P(Y=1|X=1) = 1$
Similarly, I have another joint probability table of $X and Z$ with
$P(X=1)= 0.5 $
the computations for $P(Y|X=1)$ as :
$P(Z|X=1)= \frac{P(X=1,Z)}{P(X=1)}$
and for Z = 0
$P(Z=0|X=1) = 0.6$
and for Z =1
$P(Z=1|X=1) = 0.4$
which sum up to one , $ P(Z=0|X=1) + P(Z=1|X=1) = 1$
I am trying to compute the the joint probability of $P(X=1,Y,Z)$ however, I am running into an issue that when I sum up all possible combinations of Y and Z of this joint probability, it does not sum up to one. I computed it as :
$P(X=1,Y,Z)= P(Y|X=1)P(Z|X=1)P(X=1)$
I tried with $P(X=1)= 0.325 $ from the first table and with $P(X=1)= 0.5 $ from the second table. I also tried as :
$P(X=1,Y,Z)= P(Y|X=1)P(Z|X=1)$
and it does not sum up to 1