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.
The two numbers rolled can be added to get a sum. Find P(sum is less than 4).
A. start fraction 1 over 12 end fraction
B. Start Fraction 5 over 36 End Fraction
C. Start Fraction 2 over 9 End Fraction
D. start fraction 11 over 12 end fraction.
The possible sums less than 4 are 2 and 3. There is only one way to get a sum of 2, which is rolling a 1 on both cubes. There are two ways to get a sum of 3, either by rolling a 1 and 2 or by rolling two 1's. Therefore, there are 3 favorable outcomes out of 36 total outcomes. Thus, the probability of rolling a sum less than 4 is:
P(sum < 4) = favorable outcomes/total outcomes = 3/36 = 1/12
So the answer is A.
To find the probability of getting a sum less than 4 when rolling two number cubes, we need to determine the number of favorable outcomes (sum less than 4) and divide it by the total number of possible outcomes.
From the table, we can identify the favorable outcomes: (1, 1), (1, 2), (2, 1), and (1, 3). These are the only combinations that result in a sum less than 4.
Now let's find the total number of possible outcomes. Since we are rolling two number cubes, each cube has 6 possible outcomes. Therefore, the total number of possible outcomes is 6 * 6 = 36.
So the probability of getting a sum less than 4 is:
Number of favorable outcomes / Total number of possible outcomes = 4 / 36 = 1/9
Therefore, the correct answer is C. Start Fraction 2 over 9 End Fraction.