Given that When
two dice are rolled, 36 equally likely outcomes are possible as shown
below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3)
(2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1)
(4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5)
(5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
The sum of the 36 outcomes are as follows: 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12
The number of the sums are as follows:
n(2) = 1
n(3) = 2
n(4) = 3
n(5) = 4
n(6) = 5
n(7) = 6
n(8) = 5
n(9) = 4
n(10) = 3
n(11) = 2
n(12) = 1
The probability of the sums are given as follows:
p(2) = 1/36
p(3) = 2/36 = 1/18
p(4) = 3/36 = 1/12
p(5) = 4/36 = 1/9
p(6) = 5/36
p(7) = 6/36 = 1/6
p(8) = 5/36
p(9) = 4/36 = 1/9
p(10) = 3/36 = 1/12
p(11) = 2/36 = 1/18
p(12) = 1/36
Therefore, the chart that shows the probability distribution for the sum of the two numbers is chart B.
