Suppose you roll two six-sided fair dice with faces numbered from $1$ to $6$ and take the sum of the two numbers that turn up. What is the probability that:
- the sum is $12;$
- the sum is $12$, given that the sum is even;
- the sum is $12$, given that the sum is an even number greater than $4$?
- $\frac {1}{36}, \frac {1}{18} $, and $\frac {1}{12}$, respectively
- $\frac {1}{36}, \frac {1}{18} $, and $\frac {1}{14}$, respectively
- $\frac {1}{36}, \frac {1}{16} $, and $\frac {1}{14}$, respectively
- $\frac {1}{36}, \frac {1}{16} $, and $\frac {1}{12}$, respectively