MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Concept explainers
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](https://content.bartleby.com/qna-images/question/52bde6f1-de69-4d5b-bf13-f82b423cf0e9/a9f442c2-8387-4aee-98bb-f9bf87a8721d/7y1w9n_processed.png)
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 nowThis is a popular solution!
Step by stepSolved 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.Similar questions
- Suppose that the probability that a child living in an urban area in the United States is obese is 20%. If a social worker sees 15 children living in urban areas, what is the probability that 5 are obese? Enter response as .xxxxarrow_forwardA jury of 14 people is selected from 26 people: 13 women and 13 men. What is the probability (to the nearest ten-thousandth) that the jury will have 7 men and 7 women?arrow_forwardOf the cartons produced by a company, 10% have a puncture, 5% have a smashed corner, and 0.9% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner (Type an integer or a decimal. Do not round.)arrow_forward
- A circle of friends consist of 10 individuals. 3 of them likes chocolate, 2 likes strawberry and 5 likes vanilla. what is the probability of randomly selecting 6 friends in the following manner: 1 likes chocolate, 2 likes strawberry and 3 likes vanilla?arrow_forwardSuppose that 40% of Tulane undergraduates intend to continue on to graduate school after completing their undergraduate degrees. Suppose we randomly select 20 Tulane undergraduates. Find the probability that at least 11 of the students in the sample intend to continue on to graduate school.arrow_forwardSuppose that you have 10 coins: 3 dimes, 3 quarters, and 4 nickels. Two coins are selected at random. What is the probability that you choose exactly 30 coins?arrow_forward
- Of the cartons produced by a company, 9% have a puncture, 7% have a smashed corner, and 0.5% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.arrow_forwardIn a biology class, there are 40 students, 18 of whom are female and 22 are male. If two students are randomly selected as lab partners, what is the probability that both students are of the same gender?arrow_forwardIn a survey of 1200 college students living in the dorms, 600 said that they had only a tablet in their rooms, 400 said that they had only laptop in their rooms, and 150 said that they had both a tablet and a laptop in their rooms. The remaining 50 students had neither. If a student is randomly chosen from this group, the probability that the student does have a laptop given that the student has a tablet isarrow_forward
- Suppose that 40% of Tulane undergraduates intend to continue on to graduate school after completing their undergraduate degrees. Suppose we randomly select 20 Tulane undergraduates. Find the probability that at least 10 of the students in the sample intend to continue on to graduate school.arrow_forwardSuppose a math class contains 41 students, 19 females (two of whom speak French) and 22 males (three of whom speak French). Compute the probability that a randomly selected student is male, given that the student speaks French.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman