(a) Find the probabilities of the events below. Write each answer as a single fraction. P(A) = P (B) = P(A or B) = P(A and B) = P(A) + P (B) - P(A and B) = (b) Select the probability that is equal to P (A)+P (B)-P(A and B). OP (A and B) OP (A or B) OP (B) OP (4)
(a) Find the probabilities of the events below. Write each answer as a single fraction. P(A) = P (B) = P(A or B) = P(A and B) = P(A) + P (B) - P(A and B) = (b) Select the probability that is equal to P (A)+P (B)-P(A and B). OP (A and B) OP (A or B) OP (B) OP (4)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![**Title: Venn Diagram Analysis of Student Club Memberships**
The following Venn diagram illustrates the membership of 8 students in Ms. Russell's class with respect to the Basketball Club and the Math Club.
- Kaitlin is positioned outside both circles, indicating that she is not a member of either club.
**Student Memberships:**
- **Basketball Club:**
- Boris
- Elsa
- Deshaun (also in Math Club)
- **Math Club:**
- Tammy
- Ali
- Michael
- Kira
- Deshaun (also in Basketball Club)
**Definitions:**
- Let \( A \) denote the event "the student is in the Basketball Club."
- Let \( B \) denote the event "the student is in the Math Club."
**Probability Problems:**
(a) Find the probabilities of the events below. Write each answer as a single fraction.
1. \( P(A) = \) [Probability of being in the Basketball Club]
2. \( P(B) = \) [Probability of being in the Math Club]
3. \( P(A \text{ or } B) = \) [Probability of being in either the Basketball or Math Club]
4. \( P(A \text{ and } B) = \) [Probability of being in both clubs]
**Solution Steps:**
1. Count the total number of students in each relevant group.
2. Express each probability as a fraction over the total number of students (8).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff996b914-e3a0-44c6-acc6-2ba9d8d3eb2a%2F6716e3ae-86c4-4349-9445-23589a6ba3db%2Fkj0pkcs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Venn Diagram Analysis of Student Club Memberships**
The following Venn diagram illustrates the membership of 8 students in Ms. Russell's class with respect to the Basketball Club and the Math Club.
- Kaitlin is positioned outside both circles, indicating that she is not a member of either club.
**Student Memberships:**
- **Basketball Club:**
- Boris
- Elsa
- Deshaun (also in Math Club)
- **Math Club:**
- Tammy
- Ali
- Michael
- Kira
- Deshaun (also in Basketball Club)
**Definitions:**
- Let \( A \) denote the event "the student is in the Basketball Club."
- Let \( B \) denote the event "the student is in the Math Club."
**Probability Problems:**
(a) Find the probabilities of the events below. Write each answer as a single fraction.
1. \( P(A) = \) [Probability of being in the Basketball Club]
2. \( P(B) = \) [Probability of being in the Math Club]
3. \( P(A \text{ or } B) = \) [Probability of being in either the Basketball or Math Club]
4. \( P(A \text{ and } B) = \) [Probability of being in both clubs]
**Solution Steps:**
1. Count the total number of students in each relevant group.
2. Express each probability as a fraction over the total number of students (8).
![## Probability Exercise
### (a) Find the probabilities of the events below. Write each answer as a single fraction.
- \( P(A) = \) [ ]
- \( P(B) = \) [ ]
- \( P(A \text{ or } B) = \) [ ]
- \( P(A \text{ and } B) = \) [ ]
- \( P(A) + P(B) - P(A \text{ and } B) = \) [ ]
### (b) Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \).
- \( \circ \, P(A \text{ and } B) \)
- \( \circ \, P(A \text{ or } B) \)
- \( \circ \, P(B) \)
- \( \circ \, P(A) \)
### Explanation
This exercise involves calculating and comparing probabilities of different events A and B. The goal is to understand how to find the union and intersection of two events and use this information to solve related problems.
### Diagrams
There are no diagrams or graphs associated with this exercise.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff996b914-e3a0-44c6-acc6-2ba9d8d3eb2a%2F6716e3ae-86c4-4349-9445-23589a6ba3db%2Fo8ytfij_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Probability Exercise
### (a) Find the probabilities of the events below. Write each answer as a single fraction.
- \( P(A) = \) [ ]
- \( P(B) = \) [ ]
- \( P(A \text{ or } B) = \) [ ]
- \( P(A \text{ and } B) = \) [ ]
- \( P(A) + P(B) - P(A \text{ and } B) = \) [ ]
### (b) Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \).
- \( \circ \, P(A \text{ and } B) \)
- \( \circ \, P(A \text{ or } B) \)
- \( \circ \, P(B) \)
- \( \circ \, P(A) \)
### Explanation
This exercise involves calculating and comparing probabilities of different events A and B. The goal is to understand how to find the union and intersection of two events and use this information to solve related problems.
### Diagrams
There are no diagrams or graphs associated with this exercise.
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