**important**
franklin rolls a pair of six-sided fair dice with sides numbered 1 through 6.
the probability that the sum of the numbers rolled is either even or a multiple of 5 is [11/18, 13/19, 11/36, 13/36]. the probability that the sum of the numbers rolled is either a multiple of 3 or 4 is [1/12, 1/3, 1/4, 5/9, 7/12].

11/18

5/9

Step-by-step explanation:

we will make punnette square

         dice1

    +

dice2   1       2        3       4        5       6

1            2      3        4       5        6       7

2           3      4         5       6       7        8

3           4      5         6       7       8        9

4           5      6         7       8       9        10

5           6      7         8       9      10       11

6          7       8         9       10     11        12

1)

The probability that the sum of the numbers rolled is either even or a multiple of 5

even number = 18

{(1,1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4,2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)},

and

multiple of 5 = 4

{(1,4), (2, 3), (3, 2), (4, 1), (4, 6), (5, 5), (6, 4)}

(we will skip the repeating)

18 + 4 = 22

probability = 22/36

                  = 11/18

2)

The probability that the sum of the numbers rolled is either a multiple of 3 or 4

multiple of 3 = 12

{(1, 2), (1, 5), (2, 1), (2, 4), (3, 3), (3, 6), (4, 2), (4, 5), (5, 1), (5, 4), (6, 3), (6, 6)}

and

multiple of 4 = 8

D = {(1, 3), (2, 2), (2, 6), (3, 1), (3, 5), (4, 4), (5, 3), (6, 2), (6, 6)}

(we will skip the repeating)

12 + 8 = 20

probability = 20/36

                  = 5/9

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right