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Independent or Mutually Exclusive I h S = {0, 1,2, 3, 4, 5, 6, 7} and these two events: A = {1,2, 3, 4}, and B = {3,4, 5, 6} What is P(A)? What is P(A|B)? Are A and B independent events? Yes, they are independent! O No, they are not independent! Are A and B mutually exclusive events? Yes, they are mutually exclusive! No, they are not mutually exclusive!

Independent or Mutually Exclusive I h S = {0, 1,2, 3, 4, 5, 6, 7} and these two events: A = {1,2, 3, 4}, and B = {3,4, 5, 6} What is P(A)? What is P(A|B)? Are A and B independent events? Yes, they are independent! O No, they are not independent! Are A and B mutually exclusive events? Yes, they are mutually exclusive! No, they are not mutually exclusive!

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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# Independent or Mutually Exclusive Events Consider the sample space \( S = \{0, 1, 2, 3, 4, 5, 6, 7\} \). We have two events: - \( A = \{1, 2, 3, 4\} \) - \( B = \{3, 4, 5, 6\} \) ### Questions 1. **What is \( P(A) \)?** - Input the probability of event \( A \). 2. **What is \( P(A|B) \)?** - Input the conditional probability of \( A \) given \( B \). ### Determine the Nature of Events - **Are \( A \) and \( B \) independent events?** - Yes, they are independent! - No, they are not independent! - **Are \( A \) and \( B \) mutually exclusive events?** - Yes, they are mutually exclusive! - No, they are not mutually exclusive! ### Instructions Enter your answers in the provided fields and select the appropriate options for each question. After completing, use the reset button to clear your inputs if needed.
Transcribed Image Text:# Independent or Mutually Exclusive Events Consider the sample space \( S = \{0, 1, 2, 3, 4, 5, 6, 7\} \). We have two events: - \( A = \{1, 2, 3, 4\} \) - \( B = \{3, 4, 5, 6\} \) ### Questions 1. **What is \( P(A) \)?** - Input the probability of event \( A \). 2. **What is \( P(A|B) \)?** - Input the conditional probability of \( A \) given \( B \). ### Determine the Nature of Events - **Are \( A \) and \( B \) independent events?** - Yes, they are independent! - No, they are not independent! - **Are \( A \) and \( B \) mutually exclusive events?** - Yes, they are mutually exclusive! - No, they are not mutually exclusive! ### Instructions Enter your answers in the provided fields and select the appropriate options for each question. After completing, use the reset button to clear your inputs if needed.
Expert Solution
Step 1

The value of PA is,

PA=nAnS=48=0.5

Therefore, the value of PA is 0.5.

The value of PB is,

PB=nBnS=48=0.5

The value of PB is 0.5.

The set of A∩B is,

A∩B=1,2,3,4∩3,4,5,6=3,4

The value of PA|B is,

PA|B=PA∩BPB=nA∩BnSnBnS=2848=24=0.5

Therefore, the value of PA|B is 0.5.

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