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Problem 11

# List the elements in the given set. The set of all outcomes of rolling two distinguishable dice such that the numbers add to 6

Expert verified
The elements in the given set are the pairs of numbers that add up to 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1)
See the step by step solution

## Step 1: List the possible outcomes for the first die

We roll the first die and can get any number between 1 and 6. List these numbers as possibilities: 1, 2, 3, 4, 5, and 6.

## Step 2: List the possible outcomes for the second die based on the first die's outcome

For each number we get on the first die, we need to find its corresponding number on the second die such that their sum is 6. We can do this by subtracting the first die's outcome from 6.

## Step 3: Determine outcomes

Now let's find the pairs of numbers that add up to 6: 1. When we roll a 1 on the first die, we need a 5 on the second die to get a sum of 6: (1, 5) 2. When we roll a 2 on the first die, we need a 4 on the second die to get a sum of 6: (2, 4) 3. When we roll a 3 on the first die, we need a 3 on the second die to get a sum of 6: (3, 3) 4. When we roll a 4 on the first die, we need a 2 on the second die to get a sum of 6: (4, 2) 5. When we roll a 5 on the first die, we need a 1 on the second die to get a sum of 6: (5, 1) Note that rolling a 6 on the first die is not considered because there is no corresponding number on the second die that will result in a sum of 6.

## Step 4: Write the final answer

The elements in the given set are the pairs of numbers that add up to 6: (1, 5), (2, 4), (3, 3), (4, 2), and (5, 1)

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