Let A and B be mutually exclusive events, such that P(A) = = 0.9304 and P(B) = 0.0423 . Find the following probabilities: P(A and B)= % (Round the answer to 2 decimals) P(A or B)= % (Round the answer to 2 decimals)
Let A and B be mutually exclusive events, such that P(A) = = 0.9304 and P(B) = 0.0423 . Find the following probabilities: P(A and B)= % (Round the answer to 2 decimals) P(A or B)= % (Round the answer to 2 decimals)
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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![**Probability of Mutually Exclusive Events and Their Outcomes**
When considering mutually exclusive events, it is crucial to understand that these events cannot occur simultaneously. In this exercise, we are given two events, \(A\) and \(B\), which are mutually exclusive. The probability of event \(A\), denoted as \(P(A)\), is 0.9304, and the probability of event \(B\), denoted as \(P(B)\), is 0.0423.
Given this information, the task is to find the following probabilities:
1. The probability that both events \(A\) and \(B\) occur simultaneously, represented as \(P(A \text{ and } B)\).
2. The probability that either event \(A\) or event \(B\) occurs, represented as \(P(A \text{ or } B)\).
Since events \(A\) and \(B\) are mutually exclusive, the probability that both events occur simultaneously, \(P(A \text{ and } B)\), is 0.
However, the probability that either event \(A\) or event \(B\) occurs can be found using the addition rule for mutually exclusive events:
\[ P(A \text{ or } B) = P(A) + P(B) \]
### Calculations:
1. **Probability of both events occurring (P(A and B))**:
Since \(A\) and \(B\) are mutually exclusive:
\[ P(A \text{ and } B) = 0 \]
This will be expressed as:
\[P(A \text{ and } B) = 0\% \text{ (Rounded to 2 decimals)}\]
2. **Probability of either event occurring (P(A or B))**:
Using the addition rule:
\[ P(A \text{ or } B) = P(A) + P(B) = 0.9304 + 0.0423 = 0.9727 \]
This will be expressed as:
\[ P(A \text{ or } B) = 97.27\% \text{ (Rounded to 2 decimals)}\]
These probabilities and their calculations provide a foundational understanding of how mutually exclusive events interact in probability theory.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e5613b-1a25-4b20-8027-b25d1244d9dc%2Fcff6ec00-314a-46fd-846c-d38930009ce1%2F8q7u4fp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability of Mutually Exclusive Events and Their Outcomes**
When considering mutually exclusive events, it is crucial to understand that these events cannot occur simultaneously. In this exercise, we are given two events, \(A\) and \(B\), which are mutually exclusive. The probability of event \(A\), denoted as \(P(A)\), is 0.9304, and the probability of event \(B\), denoted as \(P(B)\), is 0.0423.
Given this information, the task is to find the following probabilities:
1. The probability that both events \(A\) and \(B\) occur simultaneously, represented as \(P(A \text{ and } B)\).
2. The probability that either event \(A\) or event \(B\) occurs, represented as \(P(A \text{ or } B)\).
Since events \(A\) and \(B\) are mutually exclusive, the probability that both events occur simultaneously, \(P(A \text{ and } B)\), is 0.
However, the probability that either event \(A\) or event \(B\) occurs can be found using the addition rule for mutually exclusive events:
\[ P(A \text{ or } B) = P(A) + P(B) \]
### Calculations:
1. **Probability of both events occurring (P(A and B))**:
Since \(A\) and \(B\) are mutually exclusive:
\[ P(A \text{ and } B) = 0 \]
This will be expressed as:
\[P(A \text{ and } B) = 0\% \text{ (Rounded to 2 decimals)}\]
2. **Probability of either event occurring (P(A or B))**:
Using the addition rule:
\[ P(A \text{ or } B) = P(A) + P(B) = 0.9304 + 0.0423 = 0.9727 \]
This will be expressed as:
\[ P(A \text{ or } B) = 97.27\% \text{ (Rounded to 2 decimals)}\]
These probabilities and their calculations provide a foundational understanding of how mutually exclusive events interact in probability theory.
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