Question

LaTonda rolls two number cubes that are each numbered 1 through 6. What is the probability that the sum of the numbers on the top of both cubes will be a multiple of 4?
Select one:
1/4
1/12
1/6
1/2

Answer 1

Answer:

(A)1/4

Step-by-step explanation:

The sample space of the two dice is given as:

$(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\\(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\\(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)\\(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)\\(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\\(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)$

Total Number of Outcomes=36

The Sum is given as:

$2,3,4,5,6,7\\3,4,5,6,7,8\\4,5,6,7,8,9\\5,6,7,8,9,10\\6,7,8,9,10,11\\7,8,9,10,11,12$

Multiples of 4 are 4,8 and 12

Number of Multiples of 4=9

Therefore:

Probability that the sum of the numbers on the top of both cubes will be a multiple of 4 =9/36

=1/4.