Answer:
P(2) = 1/18
P(3) = 1/9
P(4) = 1/6
P(5) = 1/6
P(6) = 1/6
P(7) = 1/6
P(8) = 1/9
P(9) = 1/18
Step-by-step explanation:
Each die has six possible outcomes, so both dice together have 6*6 = 36 outcomes:
(1,1), (1,1), (1,2), (1,2), (1,3), (1,3),
(2,1), (2,1), (2,2), (2,2), (2,3), (2,3),
(3,1), (3,1), (3,2), (3,2), (3,3), (3,3),
(4,1), (4,1), (4,2), (4,2), (4,3), (4,3),
(5,1), (5,1), (5,2), (5,2), (5,3), (5,3),
(6,1), (6,1), (6,2), (6,2), (6,3), (6,3).
The sum of the values for each outcome is:
2, 2, 3, 3, 4, 4,
3, 3, 4, 4, 5, 5,
4, 4, 5, 5, 6, 6,
5, 5, 6, 6, 7, 7,
6, 6, 7, 7, 8, 8,
7, 7, 8, 8, 9, 9.
To find the probability of each sum, we just need to divide the number of times this sum appears over the total number of possibilities (36), so we have:
P(2) = 2/36 = 1/18
P(3) = 4/36 = 1/9
P(4) = 6/36 = 1/6
P(5) = 6/36 = 1/6
P(6) = 6/36 = 1/6
P(7) = 6/36 = 1/6
P(8) = 4/36 = 1/9
P(9) = 2/36 = 1/18
of the shaded portion.