A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time. Find the probability of rolling a 6 the first time and a 1 the second time. (Type an integer or a simplified fraction.)
A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time. Find the probability of rolling a 6 the first time and a 1 the second time. (Type an integer or a simplified fraction.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem Description:**
A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time.
---
**Solution:**
To find the probability of rolling a 6 on the first roll and a 1 on the second roll, calculate the probability of each event:
1. **Probability of rolling a 6 on the first roll:**
- A standard die has 6 faces, numbered 1 through 6.
- The probability of rolling a 6 is \( \frac{1}{6} \).
2. **Probability of rolling a 1 on the second roll:**
- Similarly, the probability of rolling a 1 is \( \frac{1}{6} \).
3. **Combined Probability:**
Since these are independent events, multiply the probabilities of each:
\[
\text{Probability of rolling a 6 then a 1} = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
**Answer:**
Type an integer or a simplified fraction: \( \frac{1}{36} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a4d4bf4-ffa5-40bf-a4b6-a19d4afcfff5%2F60054e70-e222-45f0-a23a-cd7b50be4f8b%2Fvm3feik_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time.
---
**Solution:**
To find the probability of rolling a 6 on the first roll and a 1 on the second roll, calculate the probability of each event:
1. **Probability of rolling a 6 on the first roll:**
- A standard die has 6 faces, numbered 1 through 6.
- The probability of rolling a 6 is \( \frac{1}{6} \).
2. **Probability of rolling a 1 on the second roll:**
- Similarly, the probability of rolling a 1 is \( \frac{1}{6} \).
3. **Combined Probability:**
Since these are independent events, multiply the probabilities of each:
\[
\text{Probability of rolling a 6 then a 1} = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
**Answer:**
Type an integer or a simplified fraction: \( \frac{1}{36} \)
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