Elizabeth has two identical number cubes. Both cubes have faces numbered 1 through 6. If Elizabeth rolls each cube once, what is the probability that the sum of the two numbers on the top faces will be 10?
There are a total of $6\times6=36$ possible outcomes when rolling two dice. To get a sum of 10, the two cubes must show numbers that add up to 10. These pairs are $(4,6)$ and $(5,5)$.
Each of these pairs can be rolled in two ways (for example, rolling a 4 on the first cube and a 6 on the second cube, or rolling a 6 on the first cube and a 4 on the second cube). So there are a total of 4 ways to get a sum of 10.
Therefore, the probability of rolling a sum of 10 is $\dfrac{4}{36}=\boxed{\dfrac19}$.
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Gee, I count only 3 ways to get a sum of 10 , ( 4,6 - 6,4 - 5,5)
so prob(sum of 10) = 3/36 = 1/12
You are correct! Thank you for catching that mistake. There are only three ways to get a sum of 10, and the probability is $\frac{3}{36} = \frac{1}{12}$.
To find the probability that the sum of two number cubes will be 10, we first need to determine the total number of possible outcomes when rolling two number cubes.
Step 1: Determine the total number of possible outcomes:
Since each cube has 6 faces numbered 1 through 6, the total number of possible outcomes when rolling two number cubes is 6 x 6 = 36.
Step 2: Determine the number of favorable outcomes:
To find the number of favorable outcomes (sum of two numbers equals 10), we can create a table of all possible outcomes and count the number of times the sum is 10.
Cube 1 Cube 2 Sum
4 6 10
5 5 10
6 4 10
As we can see, there are 3 favorable outcomes when the sum of two numbers is equal to 10.
Step 3: Calculate the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 3 / 36
Simplifying the fraction, we get:
Probability = 1 / 12
Therefore, the probability that the sum of the two numbers on the top faces will be 10 is 1/12.
To find the probability of rolling a sum of 10 on two number cubes, we first need to determine the number of ways we can get a sum of 10 and then divide that by the total number of possible outcomes.
Let's consider all the possible combinations of numbers on the two cubes that would result in a sum of 10:
1 + 9 (not possible since both cubes only have numbers from 1 to 6)
2 + 8 (not possible)
3 + 7 (not possible)
4 + 6 (possible)
5 + 5 (possible)
6 + 4 (possible)
7 + 3 (not possible)
8 + 2 (not possible)
9 + 1 (not possible)
From the above combinations, we see that there are 3 ways in which the sum of the two numbers is 10: 4 + 6, 5 + 5, and 6 + 4.
Now, let's calculate the total number of possible outcomes. Since each number cube has 6 faces, the total number of outcomes when rolling each cube once is 6 * 6 = 36.
Therefore, the probability of rolling a sum of 10 is 3/36, which simplifies to 1/12.
So, the probability that the sum of the two numbers on the top faces will be 10 is 1/12.