Matt 144 College Math

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 7

.

Event B

: The sum is not divisible by 2

 and not divisible by 5

.

Answer 1

Make a 6 x 6 grid with all the combinations.

Then calculate the probabilities.

Answer 2

P(2) = 1/36 = P(12)

P(3)= 2/36= P(11)

P(4)= 3/36 = P(10)

P(5) = 4/36= P(9)

P(6)= 5/36= P(8)

P(7) = 6/36

P(>7) = P(8)+P(9)+P(10)+P(11)+ P(12) = 15/36 = 5/12 = about 41.7%

P(not divisible by 2 and not divisible by 5)

= P(3)+P(7)+P(9) + P(11)

= 2/36+6/36 +4/36+ 2/36

= 14/36 = 7/18 = about %

there are 36 possible outcomes

11,

12,21,

22,31,13

23, 32,14,41

51,15,42,24,33

61,16,52,25,34,43

62,26, 53,35, 44,

63,36,54,45

64,46,55

65,56

66

1 way to get 2 or 12

2 ways get 3 or 11

3 ways to get 4 or 10

4 ways to get 5 or 9

5 ways to get 6 or 8

6 ways to get 7

divide the number of ways to get 2,3,4,5,6,7,8,9,10,11 or 12

by the total number of outcomes: 36