The image displays a word problem about probability related to a physics class. Here is the transcribed text formatted suitably for an educational website:---**Probability Problem: Physics Class**A physics class has 50 students. Of these, 17 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major.**Question:**The probability that a randomly selected student is female or a physics major is: \[ \_\_\_\_ \] (Round to three decimal places as needed.)---**Detailed Explanation:**To find the probability that a randomly selected student is either female or a physics major, we can use the principle of Inclusion-Exclusion in probability:\[ P(F \cup P) = P(F) + P(P) - P(F \cap P) \]Where:- $ P(F) $ is the probability that a student is female.- $ P(P) $ is the probability that a student is a physics major.- $ P(F \cap P) $ is the probability that a student is both female and a physics major.Step-by-Step Calculation:1. **Total Number of Students (N) = 50**2. **Number of Female Students (F) = 18**\[ P(F) = \frac{18}{50} = 0.36 \]3. **Number of Physics Majors (P) = 17**\[ P(P) = \frac{17}{50} = 0.34 \]4. **Number of Female Physics Majors (F ∩ P) = 6**\[ P(F \cap P) = \frac{6}{50} = 0.12 \]5. **Applying the Inclusion-Exclusion Principle:**\[ P(F \cup P) = 0.36 + 0.34 - 0.12 = 0.58 \]Hence, the probability that a randomly selected student is either female or a physics major is \[ 0.58 \] (rounded to three decimal places).---**Note:** It is important to carefully follow each step of probability calculation correctly to arrive at the accurate result.

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Description: The image displays a word problem about probability related to a physics class. Here is the transcribed text formatted suitably for an educational website:---**Probability Problem: Physics Class**A physics class has 50 students. Of these, 17 student

It is given that, in a physics class, there is a total of 50 students. Out of these, 17 students are…

Math

Statistics

physics class has 50 students. Of these, 17 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is Round to three decimal places as needed.)

physics class has 50 students. Of these, 17 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major. The probability that a randomly selected student is female or a physics major is Round to three decimal places as needed.)

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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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.

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Question

The image displays a word problem about probability related to a physics class. Here is the transcribed text formatted suitably for an educational website:

---

**Probability Problem: Physics Class**

A physics class has 50 students. Of these, 17 students are physics majors and 18 students are female. Of the physics majors, six are female. Find the probability that a randomly selected student is female or a physics major.

**Question:**
The probability that a randomly selected student is female or a physics major is: \[ \_\_\_\_ \] (Round to three decimal places as needed.)

---

**Detailed Explanation:**

To find the probability that a randomly selected student is either female or a physics major, we can use the principle of Inclusion-Exclusion in probability:

\[ P(F \cup P) = P(F) + P(P) - P(F \cap P) \]

Where:
- $ P(F) $ is the probability that a student is female.
- $ P(P) $ is the probability that a student is a physics major.
- $ P(F \cap P) $ is the probability that a student is both female and a physics major.

Step-by-Step Calculation:

1. **Total Number of Students (N) = 50**

2. **Number of Female Students (F) = 18**
\[ P(F) = \frac{18}{50} = 0.36 \]

3. **Number of Physics Majors (P) = 17**
\[ P(P) = \frac{17}{50} = 0.34 \]

4. **Number of Female Physics Majors (F ∩ P) = 6**
\[ P(F \cap P) = \frac{6}{50} = 0.12 \]

5. **Applying the Inclusion-Exclusion Principle:**
\[ P(F \cup P) = 0.36 + 0.34 - 0.12 = 0.58 \]

Hence, the probability that a randomly selected student is either female or a physics major is \[ 0.58 \] (rounded to three decimal places).

---

**Note:** It is important to carefully follow each step of probability calculation correctly to arrive at the accurate result.

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