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.)
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe479fc91-2cd6-4fb6-bfec-c8ec0e0a9b03%2F0099fc95-f993-4c8d-b078-1ecb5d65e62f%2Ffl7lqr_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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