Giving a test to a group of students, the grades and gender are summarized below A B C Total 15 17 Female 12 5 9 Total 31 20 | 26 Male 19 51 26 77 If one student is chosen at random, (write your answers in fraction forms) Find the probability that the student was female: Find the probability that the student was female AND got a "B": Find the probability that the student was female OR got an "A": Find the probability that the student was male GIVEN that the student got a 'B':

Giving a test to a group of students, the grades and gender are summarized below A B C Total 15 17 Female 12 5 9 Total 31 20 | 26 Male 19 51 26 77 If one student is chosen at random, (write your answers in fraction forms) Find the probability that the student was female: Find the probability that the student was female AND got a "B": Find the probability that the student was female OR got an "A": Find the probability that the student was male GIVEN that the student got a 'B':

Name: **Title: Understanding Probability with Gender and Grades****Introduc
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Description: **Title: Understanding Probability with Gender and Grades****Introduction:**In this lesson, we will explore probability concepts using a real-world example. We have a dataset that shows the grades and genders of students who took a test. Our goal is

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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Concept explainers

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

Topic Video

Question

**Title: Understanding Probability with Gender and Grades**

**Introduction:**
In this lesson, we will explore probability concepts using a real-world example. We have a dataset that shows the grades and genders of students who took a test. Our goal is to find various probabilities based on this data when a student is chosen at random.

**Data Summary:**
Below is a table summarizing the grades (A, B, C) and gender (Male, Female) of the students:

| Grade | A | B | C | Total |
|--------|----|----|----|-------|
| Male | 19 | 15 | 17 | 51 |
| Female | 12 | 5 | 9 | 26 |
| **Total** | 31 | 20 | 26 | 77 |

**Probability Questions:**

1. **Find the probability that the student was female:**
- Hint: Use the total number of females divided by the total number of students.

2. **Find the probability that the student was female AND got a "B":**
- Hint: Use the number of females who got a "B" divided by the total number of students.

3. **Find the probability that the student was female OR got an "A":**
- Hint: Add the probabilities of being female and getting an "A" and subtract the overlapping probability.

4. **Find the probability that the student was male GIVEN that the student got a "B":**
- Hint: Use the conditional probability formula, which involves dividing the number of males who got a "B" by the total number of students who got a "B".

**Graph Explanation:**
There is no graph attached to this data summary; however, the table acts as an organized way to present the categorical data of gender and grades.

**Conclusion:**
By working through these probabilities, students can better understand how to calculate and interpret different types of probabilities from categorical data. This exercise integrates knowledge of basic probability rules and conditional probability concepts.

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