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:
`(5)/(12)`

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:
`(15)/(36)` =
`(5)/(12)`

***********************************************************************************

Event B Answer:
`(1)/(2)`

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:
`(18)/(36)` =
`(1)/(2)`