**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:** 422. **Total number of females:** 183. **Total number of males:** 244. **Number of females who speak French:** 65. **Number of males who speak French:** 46. **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

Name: **Conditional Probability in a Math Class**In this example, we will e
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: **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. - Ou

given that , total students =42 , female students = 18, male students = 24. Female students who can…

Math

Statistics

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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Q: An urn contains 11 red, 10 white and 37 blue marbles. A child selects two marbles at random and…

Q: A box contains 12 chocolates: 5 dark chocolates, 4 milk chocolates, and 3 white chocolates. If two…

Q: Assume that there are 13 board members: 7 females, and 6 males including Simeoni. There are 5 tasks…

A: 1) Given that there are 13 board members in which 7 females and 6 males including Simeoni. There are…

Q: If the probability of having a female tortoise is 0.35, what is the probability of having four…

A: Given that, The probability of having a female tortoise is, p = 0.35 The no.of eggs in a nest is, n…

Q: At a local college, 76 of the male students are smokers and 114 are non-smokers. Of the female…

Q: In a sample of 1000 U.S adults, 199 think that most celebrities are good role models. Two U.S adults…

Q: Out of a class of 30 students, there are 16 students who study Latin, 21 who study German, and 7 who…

A: Given,no.of students who study Latin(L)=16no.of students who study German(G)=21no.of students who…

Q: Suppose 20% of the students in UCR commute to school every day. Among those who commute, 40% of them…

A: The objective of this question is to find the probability that a randomly selected student from UCR…

Q: In a class of 37 students, 17 are taking an AP test, 15 are taking an IB test and 6 are taking both.…

Q: A physics class has 50 students. Of these, 18 students are physics majors and 16 students are…

A: From the given information, total number of students n(S) = 50. Number of physics majors n(Physics)…

Q: A physics class has 40 students. Of these, 13 students are physics majors and 15 students are…

Q: Of the cartons produced by a company, 7% have a puncture, 4% have a smashed corner, and 1.1%…

A: It was stated that the cartons produced by a company, 7% have a puncture. The cartons produced by…

Q: Suppose a math class contains 31 students, 19 females (two of whom speak French) and 12 males (three…

A: We have given that a math class contain 31 students, 19 females( 2 speaks French) and 12 males(3…

Q: Suppose a math class contains 47 students, 24 females (four of whom speak French) and 23 males (six…

Q: Of the cartons produced by a company, 10% have a puncture, 8% have a smashed corner, and 1.3%…

Q: Suppose a math class contains 27 students, 11 who do not wear glasses (two of whom speak French) and…

A: According to the given information, we have Total number of students = 27

Q: Of the cartons produced by a company, 4% have a puncture, 7% have a smashed corner, and…

A: Given that, 4% have a puncture 7% have a smashed corner 1.3% have both a puncture and a smashed…

Q: suppose that a factory produces light bulbs and the percentage of defective lightbulbs is 3.5%. if a…

A: Probability of defective lightbulbs(p)=0.035sample ssize(n)=550Let "x" be the no. of defective…

Q: A class consists of 10 male and 30 female students. Of the 30 females, only 5 did not have pet. Six…

A: The probability of an event E is defined as the ratio of favourable number of outcomes to the total…

Q: A committee of 4 people is to be randomly selected from a group of 9 people, including Pedro. The…

A: It is given that, There is a group of 9 people including Pedro. We have to form a committee of 4…

Q: A jury pool consists of 25 people, 12 men and 13 women. Compute the probability that a randomly…

A: A jury pool consists of 25 people Number of men = 12 Number of women = 13

Q: find the probability that only three have traveled to Italy.

A: Let p be the probability that a tourist have traveled to Italy. Given that p = 0.55 Let X denotes…

Q: class consists of 50 women and 21 men. If a student is randomly selected, what is the probability…

A: According to the given information in this question, we need to find the following probability

Q: Of the cartons produced by a company, 7% have a puncture, 10% have a smashed corner, and 1.1%…

Q: From a group of 10 choldren, a team of 5 (the red team) is randomly chosen. The remaining 5 children…

A: Given from a group of 10 children, a team of 5 children is randomly chosen. The remaining 5 children…

Q: A jury pool consists of 30 people, 18 men and 12 women. Compute the probability that a randomly…

A: From the provided information, A jury pool consists 30 people. Total men = 18 Total women = 12

Q: Of 100 students, 22 can speak French, 18 can speak German, and 4 can speak both French and German.…

Q: Suppose a math class contains 27 students, 14 females (six of whom speak French) and 13 males (three…

A: Solution: From the given information, a class contains 14 females. Out of which 6 speck French.…

Q: Suppose a math class contains 25 students, 11 females (two of whom speak French) and 14 males (five…

A: GivenTotal no. of students = 25No. of females = 11No.of females whom speak french = 2No.of males =…

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

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!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

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 .xxxx
Of 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.)
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 11 of the students in the sample intend to continue on to graduate school.
Suppose 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?
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.
In 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 is
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.
Suppose 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.