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2 answers:
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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