In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they do not have a sister? Has a sister Does not have a sister Answer: Has a brother 10 6 Does not have a brother 12 2
In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they do not have a sister? Has a sister Does not have a sister Answer: Has a brother 10 6 Does not have a brother 12 2
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Conditional Probability from a Table
![### Probability of a Student Having a Brother Given They Do Not Have a Sister
In a class of students, the following data table summarizes how many students have a brother or a sister. We are interested in finding the probability that a student has a brother given that they do not have a sister.
| | **Has a brother** | **Does not have a brother** |
|------------------|------------------|---------------------------|
| **Has a sister** | 10 | 12 |
| **Does not have a sister** | 6 | 2 |
To find this probability, we can use conditional probability. Specifically, we want to find:
\[ P(\text{Has a brother} \mid \text{Does not have a sister}) \]
The formula for conditional probability is:
\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \]
In this case:
- \( A \) is the event that a student has a brother.
- \( B \) is the event that a student does not have a sister.
#### Step-by-Step Solution
1. **Identify the total number of students who do not have a sister (Event B):**
\[
\text{Total students who do not have a sister} = 6 (\text{has a brother}) + 2 (\text{does not have a brother}) = 8
\]
2. **Identify the number of students who have a brother and do not have a sister (Event A ∩ B):**
\[
\text{Students who have a brother and do not have a sister} = 6
\]
3. **Calculate the conditional probability:**
\[
P(\text{Has a brother} \mid \text{Does not have a sister}) = \frac{6}{8} = \frac{3}{4} = 0.75
\]
Therefore, the probability that a student has a brother given that they do not have a sister is \( 0.75 \) or \( 75\% \).
**Answer:**
\[ P(\text{Has a brother} \mid \text{Does not have a sister}) = 0.75 \]
---
**[ ] Answer:**
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Transcribed Image Text:### Probability of a Student Having a Brother Given They Do Not Have a Sister
In a class of students, the following data table summarizes how many students have a brother or a sister. We are interested in finding the probability that a student has a brother given that they do not have a sister.
| | **Has a brother** | **Does not have a brother** |
|------------------|------------------|---------------------------|
| **Has a sister** | 10 | 12 |
| **Does not have a sister** | 6 | 2 |
To find this probability, we can use conditional probability. Specifically, we want to find:
\[ P(\text{Has a brother} \mid \text{Does not have a sister}) \]
The formula for conditional probability is:
\[ P(A \mid B) = \frac{P(A \cap B)}{P(B)} \]
In this case:
- \( A \) is the event that a student has a brother.
- \( B \) is the event that a student does not have a sister.
#### Step-by-Step Solution
1. **Identify the total number of students who do not have a sister (Event B):**
\[
\text{Total students who do not have a sister} = 6 (\text{has a brother}) + 2 (\text{does not have a brother}) = 8
\]
2. **Identify the number of students who have a brother and do not have a sister (Event A ∩ B):**
\[
\text{Students who have a brother and do not have a sister} = 6
\]
3. **Calculate the conditional probability:**
\[
P(\text{Has a brother} \mid \text{Does not have a sister}) = \frac{6}{8} = \frac{3}{4} = 0.75
\]
Therefore, the probability that a student has a brother given that they do not have a sister is \( 0.75 \) or \( 75\% \).
**Answer:**
\[ P(\text{Has a brother} \mid \text{Does not have a sister}) = 0.75 \]
---
**[ ] Answer:**
**[Submit Answer]**
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