Question

An ordinary Fair die is a cube with the number 1 through 6 on the sides (represented by painted spots). imagine that such a die is rolled twice in succession and the face values of the two dice rolls are added together. this sum is recorded as the outcome of a single trial of random experiment.
compute the probability of each of the following events. event A: the sum is greater than 7. B: the sum is an even number

Answer 1

Event A Answer: $\frac{5}{12}$

Step-by-step explanation:

sum greater than 7 leaves are the following combinations for 8, 9, 10, 11, and 12:

8 = 26, 35, 44, 51, 62  (5 possibilities)

9 = 36, 45, 54, 63  (4 possibilities)

10 = 46, 55, 64  (3 possibilities)

11 = 56, 65  (2 possibilities)

12 = 66  (1 possibility)

This is a total of 15 possibilities out of 36 total: $\frac{15}{36}$ = $\frac{5}{12}$

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Event B Answer: $\frac{1}{2}$

Step-by-step explanation:

sum is an even number means both dice are odd or both dice are even.  That results in the following combinations:

11   13  15

22  24  26

31  33  35

42  44  46

51  53  55

62  64  66

This is a total of 18 possibilities out of 36 total: $\frac{18}{36}$ = $\frac{1}{2}$