By definition of conditional probability,


Assuming a standard 6-sided fair die,
- if
, then
means
; otherwise, - if
, then
.
Both outcomes are mutually exclusive with probability
each, hence total probability
.
Of the 36 possible outcomes, there are 6 ways to sum the integers 1-6 to get 7:
(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
and so a sum of 7 occurs
of the time.
Then the probability we want is
