Answer
$$0$$
Work Step by Step
Here, $A$ denotes the sum of numbers is $6$ and $B$ denotes the dice have opposite party.
Our aim is to calculate the conditional probability $P(A|B)$.
This can be found as: $P(A|B)=\dfrac{P(A \cap B)}{P(B)} ~~~~(1)$
We can see that $A \cap B$ shows of all outcomes that the sum of numbers is $6$ and the dice have opposite party. This means that $A \cap B=\{0\}$
So, $P(A \cap B)=\dfrac{n(A \cap B)}{n(S)}=0$
We can see that there are $18$ possible pairs for the dice have opposite party. This means that $n(B)=12$.
So, $P(B)=\dfrac{n(B)}{n(S)}=\dfrac{18}{36}$
Thus, the equation (1) becomes:
$P(A~|~B)=\dfrac{P(A \cap B)}{P(B)} =\dfrac{0}{18/36}=0$
