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Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 14 6 19 39 Female 3 4 20 27 Total 17 10 39 66 If one student is chosen at random, Find the probability that the student got a C: Find the probability that the student was male AND got a "C": Find the probability that the student was female OR got an "A": If one student is chosen at random, find the probability that the student got a 'C' GIVEN they are female:

Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 14 6 19 39 Female 3 4 20 27 Total 17 10 39 66 If one student is chosen at random, Find the probability that the student got a C: Find the probability that the student was male AND got a "C": Find the probability that the student was female OR got an "A": If one student is chosen at random, find the probability that the student got a 'C' GIVEN they are female:

MATLAB: An Introduction with Applications
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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**Educational Website Content: Probability and Statistics** ## Example Scenario: Analyzing Test Scores ### Dataset Summary We are given data on the grades achieved by a group of students, categorized by gender. The data is summarized in the table below: | | A | B | C | Total | |--------|---|---|----|-------| | **Male** | 14 | 6 | 19 | 39 | | **Female** | 3 | 4 | 20 | 27 | | **Total** | 17 | 10 | 39 | 66 | ### Probabilities Using the data from the table, we can answer the following probability questions: **1. Find the probability that the student got a C:** P(C) = (Number of students who got a C) / (Total number of students) **2. Find the probability that the student was male AND got a "C":** P(Male AND C) = (Number of male students who got a C) / (Total number of students) **3. Find the probability that the student was female OR got an "A":** P(Female OR A) = (Number of females + Number of students who got an A - Number of female students who got an A) / (Total number of students) **4. If one student is chosen at random, find the probability that the student got a 'C' GIVEN they are female:** P(C | Female) = (Number of female students who got a C) / (Total number of female students) --- ### Worked Example **1. Probability that a randomly chosen student got a C:** \[ P(C) = \frac{39}{66} \] **2. Probability that a male student got a "C":** \[ P(Male \text{ AND } C) = \frac{19}{66} \] **3. Probability that a student was female OR got an "A":** \[ P(Female \text{ OR } A) = \frac{27 + 17 - 3}{66} \] **4. Probability that a student got a 'C' given they are female:** \[ P(C | Female) = \frac{20}{27} \]
Transcribed Image Text:**Educational Website Content: Probability and Statistics** ## Example Scenario: Analyzing Test Scores ### Dataset Summary We are given data on the grades achieved by a group of students, categorized by gender. The data is summarized in the table below: | | A | B | C | Total | |--------|---|---|----|-------| | **Male** | 14 | 6 | 19 | 39 | | **Female** | 3 | 4 | 20 | 27 | | **Total** | 17 | 10 | 39 | 66 | ### Probabilities Using the data from the table, we can answer the following probability questions: **1. Find the probability that the student got a C:** P(C) = (Number of students who got a C) / (Total number of students) **2. Find the probability that the student was male AND got a "C":** P(Male AND C) = (Number of male students who got a C) / (Total number of students) **3. Find the probability that the student was female OR got an "A":** P(Female OR A) = (Number of females + Number of students who got an A - Number of female students who got an A) / (Total number of students) **4. If one student is chosen at random, find the probability that the student got a 'C' GIVEN they are female:** P(C | Female) = (Number of female students who got a C) / (Total number of female students) --- ### Worked Example **1. Probability that a randomly chosen student got a C:** \[ P(C) = \frac{39}{66} \] **2. Probability that a male student got a "C":** \[ P(Male \text{ AND } C) = \frac{19}{66} \] **3. Probability that a student was female OR got an "A":** \[ P(Female \text{ OR } A) = \frac{27 + 17 - 3}{66} \] **4. Probability that a student got a 'C' given they are female:** \[ P(C | Female) = \frac{20}{27} \]
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