A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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![**Reworking Probability Problem with Tree Diagrams**
To tackle problem 18 from section 3.3 of your textbook, you will fill in missing probabilities using a tree diagram. Start by constructing figure 3.11 where the first outcome is one of (A, B, C) and the second outcome in each case is one of (1, 2, 3). Note that outcome C is limited to options 1 or 2.
Apply these probabilities:
- \( Pr[A1] = \frac{1}{12} \)
- \( Pr[2|A] = \frac{1}{3} \)
- \( Pr[A2] = \frac{1}{12} \)
- \( Pr[A3] = \frac{1}{12} \)
- \( Pr[B1] = \frac{1}{12} \)
- \( Pr[2|B] = \frac{1}{3} \)
- \( Pr[B3] = \frac{1}{12} \)
- \( Pr[C1] = \frac{1}{12} \)
- \( Pr[C2] = \frac{1}{8} \)
**Find the following missing probabilities:**
1. \( Pr[A] = \) [ ]
2. \( Pr[1|A] = \) [ ]
3. \( Pr[2|A] = \) [ ]
4. \( Pr[B] = \) [ ]
**Detailed Explanation of Diagrams:**
The problem involves using a three-layer tree diagram. Begin at a root, branching into outcomes A, B, and C. From each of those branches, additional branches represent values 1, 2, or 3 based on the given probabilities.
This exercise involves not just computation, but a strategic visualization of probabilities through a tree diagram, providing a solid foundation for understanding complex probability scenarios.](https://content.bartleby.com/qna-images/question/603fbc9e-cdba-4fa0-b3dd-1f2ec72dd924/c2e81763-bb93-413e-bd99-6ea023a6b092/kxml02_processed.jpeg)
Transcribed Image Text:**Reworking Probability Problem with Tree Diagrams**
To tackle problem 18 from section 3.3 of your textbook, you will fill in missing probabilities using a tree diagram. Start by constructing figure 3.11 where the first outcome is one of (A, B, C) and the second outcome in each case is one of (1, 2, 3). Note that outcome C is limited to options 1 or 2.
Apply these probabilities:
- \( Pr[A1] = \frac{1}{12} \)
- \( Pr[2|A] = \frac{1}{3} \)
- \( Pr[A2] = \frac{1}{12} \)
- \( Pr[A3] = \frac{1}{12} \)
- \( Pr[B1] = \frac{1}{12} \)
- \( Pr[2|B] = \frac{1}{3} \)
- \( Pr[B3] = \frac{1}{12} \)
- \( Pr[C1] = \frac{1}{12} \)
- \( Pr[C2] = \frac{1}{8} \)
**Find the following missing probabilities:**
1. \( Pr[A] = \) [ ]
2. \( Pr[1|A] = \) [ ]
3. \( Pr[2|A] = \) [ ]
4. \( Pr[B] = \) [ ]
**Detailed Explanation of Diagrams:**
The problem involves using a three-layer tree diagram. Begin at a root, branching into outcomes A, B, and C. From each of those branches, additional branches represent values 1, 2, or 3 based on the given probabilities.
This exercise involves not just computation, but a strategic visualization of probabilities through a tree diagram, providing a solid foundation for understanding complex probability scenarios.
![The image contains five mathematical probability expressions, each followed by an empty input box for entering answers. Here are the expressions provided:
1. \( \text{(5) } Pr[1|B] = \)
2. \( \text{(6) } Pr[3|B] = \)
3. \( \text{(7) } Pr[B2] = \)
4. \( \text{(8) } Pr[C] = \)
5. \( \text{(9) } Pr[1|C] = \)
6. \( \text{(10) } Pr[2|C] = \)
All expressions have empty boxes next to them, indicating where answers can be filled in. Each box also features a grid icon, suggesting perhaps a calculator or reference tool is available to assist with the input.](https://content.bartleby.com/qna-images/question/603fbc9e-cdba-4fa0-b3dd-1f2ec72dd924/c2e81763-bb93-413e-bd99-6ea023a6b092/tiim2cr_processed.png)
Transcribed Image Text:The image contains five mathematical probability expressions, each followed by an empty input box for entering answers. Here are the expressions provided:
1. \( \text{(5) } Pr[1|B] = \)
2. \( \text{(6) } Pr[3|B] = \)
3. \( \text{(7) } Pr[B2] = \)
4. \( \text{(8) } Pr[C] = \)
5. \( \text{(9) } Pr[1|C] = \)
6. \( \text{(10) } Pr[2|C] = \)
All expressions have empty boxes next to them, indicating where answers can be filled in. Each box also features a grid icon, suggesting perhaps a calculator or reference tool is available to assist with the input.
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