I roll a fair die twice and obtain two numbers
X1= result of the first roll and X2 = result of the second roll. Given that I know X1+X2 = 12, what is the probability that X₁ is odd.

To solve the problem, let's break it down step by step:

### Step 1: Identify the possible outcomes.
You know that the sum of the results from rolling the two dice is \( X_1 + X_2 = 12 \).

The possible outcomes for two dice rolls that sum to 12 are:
- \( (6, 6) \)

This is the only pair where the sum of the two numbers is 12, since the largest number possible on a die is 6.

### Step 2: Analyze the possible values for \( X_1 \).
Given that the sum is \( X_1 + X_2 = 12 \), the only outcome is \( (6, 6) \), meaning \( X_1 = 6 \) and \( X_2 = 6 \).

### Step 3: Check if \( X_1 \) is odd.
The value of \( X_1 \) is 6, which is even, not odd.

### Step 4: Calculate the probability.
Since \( X_1 = 6 \) is the only possible value and it's even, the probability that \( X_1 \) is odd is:

\[
P(X_1 \text{ is odd}) = 0
\]

Thus, the probability that \( X_1 \) is odd given that \( X_1 + X_2 = 12 \) is 0.

---

Would you like more details, or have any questions about the solution?

Here are five related questions to expand on this:
1. What is the probability that \( X_1 + X_2 = 7 \)?
2. What is the probability that both dice show an odd number?
3. How does the probability change if you know \( X_1 \) is greater than \( X_2 \)?
4. What is the probability that the sum of two rolls is at least 10?
5. How do you calculate conditional probabilities when rolling dice?

**Tip:** When rolling dice, identifying all possible outcomes before applying conditions is key to correctly calculating probabilities.

I roll a fair die twice and obtain two numbers X1 = result of the first roll and X2 = result of the second roll. Given that I know X1 + X2 = 12, what is the probability that X₁ is odd?

Solve a probability problem where two dice are rolled, and X₁ + X₂ = 12. Learn the step-by-step breakdown of how to calculate the probability that X₁ is odd, using key concepts in probability and combinatorics. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation