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 two odd numbers?
A. one-ninth
B. one-fourth
C. one-third
D. start fraction 4 over 9 end fraction
There are 3 odd numbers on a number cube (1, 3, and 5). Therefore, there are 3 possible odd numbers that could be rolled on each cube, and a total of 3 x 3 = 9 possible outcomes where both rolls result in odd numbers.
There are a total of 6 x 6 = 36 possible outcomes in the sample space.
Therefore, the probability of rolling two odd numbers is 9/36, which simplifies to 1/4 or one-fourth.
The answer is B.
To find the probability that the roll will result in two odd numbers, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
There are 6 rows and 6 columns in the table, so there are a total of 6 x 6 = 36 possible outcomes.
To count the number of favorable outcomes, we need to find the ordered pairs where both elements are odd numbers. There are 3 odd numbers in each row and each column (1, 3, 5), so the number of favorable outcomes is 3 x 3 = 9.
Therefore, the probability of rolling two odd numbers is 9/36 = 1/4.
The correct answer is B. one-fourth.