**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

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

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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

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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

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