.
The full space of events is the set of all pairs (m,n), where m and n are integers between 1 and 6 inclusively
- possible outcomes from each dice.
Thus the full space of events has 6*6 = 36 elements, each with the probability of
.
The probability of getting the sum at least of 3 is the sum of probabilities of getting 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 (maximum).
The complement event is to get the sum of 2, which is possible for only one configuration (m,n) = (1,1) of the base space of events.
So, the probability of getting this complement event is
.
Hence, the probability that the problem asking for is
=
. ANSWER
The problem is solved.
Thus using the complement space of events, we are free from the need to analyse all 35 events of the base space.