An ordinary (fair) die is a cube with the numbers through on the sides (represented by painted spots). Imagine that such a

Question

An ordinary (fair) die is a cube with the numbers 1

 through 6

 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.Compute the probability of each of the following events.

Event A

: The sum is greater than 6

.

Event B

: The sum is divisible by 3

 or 6

 (or both).

Write your answers as exact fractions.

P(A) = ?

P(B) = ?

Answer 1

possible outcomes

11

12

13

14

15

16 only 1 out of 6 is greater than 6, 2 are divisible by 3

21

22

23

24

25

26 only 2 of 6 are greater than 6, 2 divisible by 3

31

32

33

34

35

36 3 of 6 are greater than 6, 2 divisible by 3

41

42

43

44

45

46 4 of 6 are greater than 6, 2 divisible by 3

51

52

53

54

55

56 5 of 6 are greater than 6, 2 divisible by 3

61

62

63

64

65

66 all 6 are greater than 6, 2 divisible by 3

36 outcomes with 6+5+4+3+2+1 = 21 greater than 6

P(A) = 21/36 = 7/12

P(B) = 1/3

2 of 6 outcomes are divisible by 3 or 6