Juan has two number cubes, each with faces 1,2,3,4,5,6. What is the probability he can roll the cubes so that the sum of the faces showing equals 11?
To find the probability that Juan can roll the number cubes and get a sum of 11, we need to determine the number of favorable outcomes and the total number of possible outcomes.
1. Determine the number of favorable outcomes:
We need to find the combinations of numbers on each cube that add up to 11. These include:
- Cube 1: 5 + 6 = 11 or 6 + 5 = 11 (2 favorable outcomes)
- Cube 2: 5 + 6 = 11 or 6 + 5 = 11 (2 favorable outcomes)
Since we have two cubes, we will consider all possible combinations of outcomes. For each favorable outcome on cube 1, we need a matching favorable outcome on cube 2. Hence, the total number of favorable outcomes is (2 favorable outcomes on cube 1) * (2 favorable outcomes on cube 2) = 4 favorable outcomes.
2. Determine the total number of possible outcomes:
Since each cube has 6 faces, the total number of possible outcomes on each cube is 6.
Since we have two cubes, the total number of possible outcomes is 6 * 6 = 36.
3. Calculate the probability:
The probability is the ratio of favorable outcomes to total outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
In this case, the probability is 4 favorable outcomes / 36 possible outcomes.
Simplifying, the probability Juan can roll the cubes and get a sum of 11 is 1/9 or approximately 0.1111 (rounded to four decimal places).
To find the probability of rolling the two number cubes and getting a sum of 11, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the favorable outcomes:
Let's list all the possible ways to get a sum of 11 with two number cubes:
- (5, 6)
- (6, 5)
So there are two favorable outcomes.
Step 2: Determine the total number of outcomes:
Since each number cube has 6 faces, there are a total of 6 possible outcomes for each cube. Thus, the total number of outcomes for the two cubes is 6 x 6 = 36.
Step 3: Calculate the probability:
To find the probability, divide the number of favorable outcomes by the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 2 / 36
Probability = 1 / 18
Therefore, the probability that Juan can roll the two number cubes and get a sum of 11 is 1/18.