Suppose a math class contains 42 students, 18 females (six of whom speak French) and 24 males (four of whom speak French). Compute the probability that a randomly selected student is female, given that the student speaks French.
Suppose a math class contains 42 students, 18 females (six of whom speak French) and 24 males (four of whom speak French). Compute the probability that a randomly selected student is female, given that the student speaks French.
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section: Chapter Questions
Problem 2P: Family Planning A intend to have two children. What is tie probability that they will have child of...
Related questions
Concept explainers
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Topic Video
Question
![**Conditional Probability in a Math Class**
In this example, we will explore conditional probability in the context of a math class.
**Problem Statement:**
Suppose a math class contains 42 students, with details as follows:
- There are 18 females.
- Out of these 18 females, 6 speak French.
- There are 24 males.
- Out of these 24 males, 4 speak French.
The total number of students who speak French (both male and female) is 10.
We need to compute the probability that a randomly selected student is female, given that the student speaks French.
**Let's break down the problem:**
1. **Total number of students:** 42
2. **Total number of females:** 18
3. **Total number of males:** 24
4. **Number of females who speak French:** 6
5. **Number of males who speak French:** 4
6. **Total number of students who speak French:** 6 (females) + 4 (males) = 10
**Approach to solve:**
To find the probability that a randomly selected student is female, given that the student speaks French, we use the formula for conditional probability:
\[ P(\text{Female} | \text{Speak French}) = \frac{P(\text{Female and Speak French})}{P(\text{Speak French})} \]
where:
- \( P(\text{Female and Speak French}) \) is the probability that a student is both female and speaks French.
- \( P(\text{Speak French}) \) is the probability that a student speaks French.
**Calculations:**
1. \( P(\text{Female and Speak French}) = \frac{\text{Number of females who speak French}}{\text{Total number of students}} = \frac{6}{42} = \frac{1}{7} \)
2. \( P(\text{Speak French}) = \frac{\text{Total number of students who speak French}}{\text{Total number of students}} = \frac{10}{42} = \frac{5}{21} \)
So,
\[ P(\text{Female} | \text{Speak French}) = \frac{P(\text{Female and Speak French})}{P(\text{Speak French})} = \frac{\frac{1}{7}}{\frac{5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F52bde6f1-de69-4d5b-bf13-f82b423cf0e9%2Fa9f442c2-8387-4aee-98bb-f9bf87a8721d%2F7y1w9n_processed.png&w=3840&q=75)
Transcribed Image Text:**Conditional Probability in a Math Class**
In this example, we will explore conditional probability in the context of a math class.
**Problem Statement:**
Suppose a math class contains 42 students, with details as follows:
- There are 18 females.
- Out of these 18 females, 6 speak French.
- There are 24 males.
- Out of these 24 males, 4 speak French.
The total number of students who speak French (both male and female) is 10.
We need to compute the probability that a randomly selected student is female, given that the student speaks French.
**Let's break down the problem:**
1. **Total number of students:** 42
2. **Total number of females:** 18
3. **Total number of males:** 24
4. **Number of females who speak French:** 6
5. **Number of males who speak French:** 4
6. **Total number of students who speak French:** 6 (females) + 4 (males) = 10
**Approach to solve:**
To find the probability that a randomly selected student is female, given that the student speaks French, we use the formula for conditional probability:
\[ P(\text{Female} | \text{Speak French}) = \frac{P(\text{Female and Speak French})}{P(\text{Speak French})} \]
where:
- \( P(\text{Female and Speak French}) \) is the probability that a student is both female and speaks French.
- \( P(\text{Speak French}) \) is the probability that a student speaks French.
**Calculations:**
1. \( P(\text{Female and Speak French}) = \frac{\text{Number of females who speak French}}{\text{Total number of students}} = \frac{6}{42} = \frac{1}{7} \)
2. \( P(\text{Speak French}) = \frac{\text{Total number of students who speak French}}{\text{Total number of students}} = \frac{10}{42} = \frac{5}{21} \)
So,
\[ P(\text{Female} | \text{Speak French}) = \frac{P(\text{Female and Speak French})}{P(\text{Speak French})} = \frac{\frac{1}{7}}{\frac{5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
