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
To find the probability that the roll will result in both numbers being the same, we need to determine the number of favorable outcomes (where both numbers are the same) and the total number of possible outcomes.
In this case, there are 6 favorable outcomes because each number from 1 to 6 can be rolled twice (e.g., (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)).
The total number of possible outcomes can be calculated by multiplying the number of possible outcomes for the first number (6) by the number of possible outcomes for the second number (6), which equals 6 * 6 = 36.
Therefore, the probability that the roll will result in both numbers being the same is 6/36, which simplifies to 1/6.
So, the correct answer is:
A. start fraction 1 over 6 end fraction