Answer
$\dfrac{1}{10}$
Work Step by Step
Here, $A$ denotes the sum of the numbers is $5$ and $B$ denotes the green dice which is not $1$.
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, $P(A \cap B)=\dfrac{n(A \cap B}{n(S)}=\dfrac{3}{36}=\dfrac{1}{12}$
and $P(B)=\dfrac{n(B)}{n(S)}=\dfrac{30}{36}=\dfrac{5}{6}$
Thus, the equation (1) becomes:
$P(A~|~B)=\dfrac{P(A \cap B)}{P(B)} =\dfrac{1/12}{5/6}=\dfrac{1}{10}$
