The sample space for a roll of two number cubes is shown in the table.
A 6 by 6 table of ordered pairs is shown.
• A single ordered pair appears in each cell of the table.
In row one, the first element of each ordered pair is 1. This pattern continues through row 6, where the first element in each ordered pair is 6.
• In column one, the second element in each ordered pair is 1. This pattern continues through column 6, where the second element in each ordered pair is 6.
What is the probability that the roll will result in both numbers being the same?
A. start fraction 1 over 6 end fraction
B. one-third
C. start fraction 7 over 18 end fraction
D. Start Fraction 2 over 3 End Fraction.
There are 6 possible outcomes where both numbers are the same: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
The total number of outcomes is 6*6 = 36.
Therefore, the probability of rolling both numbers the same is 6/36 = 1/6, which is answer choice A.
To find the probability that the roll will result in both numbers being the same, we need to determine the number of outcomes where the numbers on both number cubes are equal, and then divide that by the total number of possible outcomes.
Looking at the table, we see that there are 36 cells in total, representing all possible outcomes. Out of these 36 outcomes, there are 6 instances where both numbers are the same. These occur on the main diagonal of the table, where the row number is equal to the column number.
Therefore, the probability that the roll will result in both numbers being the same is given by the number of favorable outcomes (6) divided by the total number of possible outcomes (36):
Probability = 6/36 = 1/6
So, the correct answer is A. start fraction 1 over 6 end fraction.