Answer
$\dfrac{1}{6}$
Work Step by Step
Here, $A$ denotes the sum of the numbers is $6$ and $B$ denotes the green dice is either $3$ or $4$.
Our aim is to calculate the conditional probability $P(A|B)$.
This can be found as: $P(A|B)=\dfrac{P(A \cap B)}{P(B)} ~~~~(1)$
Now, $P(A \cap B)=\dfrac{n(A \cap B)}{n(S)}=\dfrac{2}{36}=\dfrac{1}{18}$
We can see that there are $12$ possible pairs for the green dice is either $3$ or $4$. This means that $n(B)=12$
Therefore, $P(B)=\dfrac{n(B)}{n(S)}=\dfrac{12}{36}=\dfrac{1}{3}$
Thus, the equation (1) becomes:
$P(A~|~B)=\dfrac{P(A \cap B)}{P(B)} =\dfrac{1/18}{1/3}=\dfrac{1}{6}$
