Question

You roll two fair six-sided dice. What is the probability that the sum of the two dice values is exactly five? Be sure to count all possible outcomes. (Hint: The event space has 36 distinct outcomes).

Answer 1

sum of the dice	list of outcomes favourable to sum	number of outcomes favourable to sum
2	(1,1)	1
3	(1,2),(2,1)	2
4	(1,3),(2,2),(3,1)	3
5	(1,4)(2,3),(3,2),(4,1)	4
6	(1,5),(2,4),(3,3),(4,2),(5,1)	5
7	(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)	6
8	(2,6),(3,5),(4,4),(5,3),(6,2)	5
9	(3,6),(4,5),(5,4),(6,3)	4
10	(4,6),(5,5),(6,4)	3
11	(5,6),(6,5)	2
12	(6,6)	1

Total number of distinct case is 36

Number of case in which sum is 5 =4