Math Problem Statement
I roll a fair die twice and obtain two numbers
X 1 X 1 = result of the first roll and X 2 X 2 = result of the second roll.
Given that I know X 1 + X 2
12 X 1 +X 2 =12, what is the probability that X 1 X 1 is odd.
Solution
Given the problem:
- is the result of the first die roll.
- is the result of the second die roll.
- You know that .
- You want to find the probability that is odd.
Step 1: List Possible Combinations of and
Since , the possible pairs of , where each number comes from a fair die (numbers 1 through 6), are:
The only combination that satisfies this equation is and .
Step 2: Determine if is Odd
For , , which is even, not odd.
Step 3: Conclusion
Since there is only one possible outcome, , and is even, the probability that is odd is:
The probability is 0.
Would you like further clarification or have any additional questions? Here are some related questions you might consider:
- What is the probability that is odd given the same conditions?
- How does the result change if I roll a die three times and sum the results?
- What is the probability of obtaining an even number for both dice rolls?
- How would the problem change if the sum were a different number?
- What is the probability that both dice rolls give the same result?
Tip: When working with probabilities involving dice, listing all possible outcomes helps identify patterns and constraints quickly.
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Math Problem Analysis
Mathematical Concepts
Probability
Combinatorics
Formulas
P(event) = favorable outcomes / total outcomes
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 6-8