The two numbers rolled can be added to get a sum. Find P(sum is even).
A. one-fourth
B. start fraction 15 over 36 end fraction
C. one-half
D. start fraction 3 over 4 end fraction
To get an even sum, we need to have one even and one odd number when we add the two dice together. There are 3 even numbers and 3 odd numbers on a standard die, so the probability of rolling an even and an odd is:
3/6 × 3/6 = 9/36
And the probability of rolling an odd and an even (which is the same probability) is also 9/36. So the total probability of rolling an even sum is:
9/36 + 9/36 = 18/36 = 1/2
Therefore, the answer is (C) one-half.
While remodeling the house, you have 3 choices of paint color, 4 choices of carpet color, and 5 choices of furniture style. How many different groupings will you be able to make using one paint color, one carpet color, and one furniture style?
A. 20
B. 50
C. 60
D. 80
To find the total number of groupings, we need to multiply the number of choices for each category:
3 choices of paint color × 4 choices of carpet color × 5 choices of furniture style = 60
Therefore, there are 60 different groupings possible.
The answer is (C) 60.
To find the probability that the sum of two rolled numbers is even, we need to determine the number of favorable outcomes (sums that are even) and divide it by the total number of possible outcomes.
Let's consider all possible outcomes when two numbers are rolled on a fair, six-sided die:
The possible outcomes for rolling the first number are 1, 2, 3, 4, 5, and 6. For each of these outcomes, the second number could also be any of these six values.
To determine the total number of possible outcomes, we multiply the number of possibilities for the first roll (6) by the number of possibilities for the second roll (also 6). So, there are a total of 6 * 6 = 36 possible outcomes.
Now, let's consider the favorable outcomes: sums that are even. To get an even number, we can have:
- An even number for the first roll and an even number for the second roll: There are three even numbers (2, 4, and 6). Since there are six choices for each roll, there are 3 * 3 = 9 favorable outcomes in this case.
- An odd number for the first roll and an odd number for the second roll: There are three odd numbers (1, 3, and 5). Again, there are 3 * 3 = 9 favorable outcomes in this case.
Adding the favorable outcomes from both cases, we have a total of 9 + 9 = 18 favorable outcomes.
Finally, to find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
P(sum is even) = favorable outcomes / total outcomes = 18 / 36 = 1/2
Therefore, the correct answer is C. one-half.