Given that P(A)=3, P(B)=, and P(A and B)=10, find P(A or B). 7 ㅇ 10 45 3/10 5 34
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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![**Question:**
Given that P(A) = \( \frac{3}{5} \), P(B) = \( \frac{1}{5} \), and P(A and B) = \( \frac{1}{10} \), find P(A or B).
**Options:**
1. \( \frac{7}{10} \)
2. \( \frac{4}{5} \)
3. \( \frac{3}{5} \)
4. \( \frac{3}{4} \)
**Solution:**
To find P(A or B), we use the formula for the probability of the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Given:
- P(A) = \( \frac{3}{5} \)
- P(B) = \( \frac{1}{5} \)
- P(A and B) = \( \frac{1}{10} \)
Substitute the values into the formula:
\[ P(A \cup B) = \frac{3}{5} + \frac{1}{5} - \frac{1}{10} \]
Convert the fractions to a common denominator to simplify the calculation. The common denominator for 5 and 10 is 10:
\[ \frac{3}{5} = \frac{6}{10} \]
\[ \frac{1}{5} = \frac{2}{10} \]
Now substitute these into the formula:
\[ P(A \cup B) = \frac{6}{10} + \frac{2}{10} - \frac{1}{10} \]
Combine the fractions:
\[ P(A \cup B) = \frac{6 + 2 - 1}{10} = \frac{7}{10} \]
So the probability P(A or B) is:
\[ \boxed{\frac{7}{10}} \]
In the provided options, the correct answer should be selected.
Therefore, the correct answer should be \( \frac{7}{10} \), however, noting that the second option \( \frac{4}{5} \) is marked, the proper understanding and selection process should have identified \( \frac{7}{10} \). Therefore, there is a marked discrepancy to be corrected and the right answer is indeed \( \frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11b3ac0d-2603-4899-810b-1b144399767c%2F652c7533-1260-46df-8cc1-45c9666114dc%2Fr8nw79p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Given that P(A) = \( \frac{3}{5} \), P(B) = \( \frac{1}{5} \), and P(A and B) = \( \frac{1}{10} \), find P(A or B).
**Options:**
1. \( \frac{7}{10} \)
2. \( \frac{4}{5} \)
3. \( \frac{3}{5} \)
4. \( \frac{3}{4} \)
**Solution:**
To find P(A or B), we use the formula for the probability of the union of two events:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Given:
- P(A) = \( \frac{3}{5} \)
- P(B) = \( \frac{1}{5} \)
- P(A and B) = \( \frac{1}{10} \)
Substitute the values into the formula:
\[ P(A \cup B) = \frac{3}{5} + \frac{1}{5} - \frac{1}{10} \]
Convert the fractions to a common denominator to simplify the calculation. The common denominator for 5 and 10 is 10:
\[ \frac{3}{5} = \frac{6}{10} \]
\[ \frac{1}{5} = \frac{2}{10} \]
Now substitute these into the formula:
\[ P(A \cup B) = \frac{6}{10} + \frac{2}{10} - \frac{1}{10} \]
Combine the fractions:
\[ P(A \cup B) = \frac{6 + 2 - 1}{10} = \frac{7}{10} \]
So the probability P(A or B) is:
\[ \boxed{\frac{7}{10}} \]
In the provided options, the correct answer should be selected.
Therefore, the correct answer should be \( \frac{7}{10} \), however, noting that the second option \( \frac{4}{5} \) is marked, the proper understanding and selection process should have identified \( \frac{7}{10} \). Therefore, there is a marked discrepancy to be corrected and the right answer is indeed \( \frac
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