<h3><u>
Answer:</u></h3>
Hence, the probability that the numbers showing face-up after the roll will have a sum of 9 is:
1/9
<h3><u>
Step-by-step explanation:</u></h3>
William has a pair of identical number cubes. the faces of each cube are numbered 1 through 6.
Now when he rolls two cubes together the possible outcomes are:
(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)
Now, the outcomes having sum 9 is:
(3,6) (6,3) (5,4) (4,5)
Hence total outcomes=36
Number of outcomes having sum 9 ( Number of favorable outcomes)=4
Hence,
Probability( sum is 9)=Number of favorable outcomes/Total outcomes.
= 4/36=1/9
Hence, the answer is:
1/9
