11. Elizabeth has two identical number cubes. Both cubes have faces numbered 1 through 6. If Elizabeth rolls (1 point) each cube once, what is the probability that the sum of the two numbers on the top faces will be 10?
There are 36 possible outcomes (6 outcomes for the first cube and 6 outcomes for the second cube).
To get a sum of 10, Elizabeth can roll:
- 4 on the first cube and 6 on the second cube
- 5 on the first cube and 5 on the second cube
- 6 on the first cube and 4 on the second cube
Therefore, there are 3 favorable outcomes.
The probability of getting a sum of 10 is:
3 favorable outcomes / 36 possible outcomes = 1/12
To find the probability of rolling a sum of 10 with two identical number cubes, we need to determine the number of favorable outcomes (where the sum is 10) and the total number of possible outcomes.
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 is 6 * 6 = 36.
Step 2: Determine the number of favorable outcomes.
To get a sum of 10, we can have the following combinations of numbers on the two cubes:
- (4, 6)
- (5, 5)
- (6, 4)
Therefore, there are 3 favorable outcomes.
Step 3: Calculate the probability.
The probability is the number of favorable outcomes divided by the total number of possible outcomes.
Probability = number of favorable outcomes / total number of possible outcomes
= 3 / 36
= 1/12
So, the probability that the sum of the two numbers on the top faces will be 10 is 1/12.
To calculate the probability of getting a sum of 10 when rolling two identical number cubes, you need to determine the number of favorable outcomes (the sum of two numbers is 10) and the total number of possible outcomes.
To find the number of favorable outcomes, you can identify all the possible combinations that yield a sum of 10. The pairs of numbers that result in a sum of 10 are (4, 6), (5, 5), and (6, 4). There are three favorable outcomes.
To find the total number of possible outcomes, you need to calculate all the unique combinations of numbers on the two number cubes. Since each number cube has 6 faces, there are 6 possible outcomes for each cube. Since the number cubes are identical, you multiply the number of possible outcomes for one cube by itself. Therefore, there are a total of 6 * 6 = 36 possible outcomes.
Now that you have the number of favorable outcomes (3) and the total number of possible outcomes (36), you can calculate the probability 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, the probability of getting a sum of 10 when rolling two identical number cubes is 1/12.