Civil Engineering (CE) Exam > Civil Engineering (CE) Questions > If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) ...
Start Learning for Free
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________
- a)1
- b)2/3
- c)1/2
- d)5/6
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ___...
We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
⇒ 8/11 = 7/11 + 6/11 – P(A∩B)
⇒ P(A∩B) = 13/11 – 7/11
⇒ P(A∩B) = 6/11
P(A|B) = (6/11) / (6/11).
P(A|B) = 1.
Also P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability)
⇒ 8/11 = 7/11 + 6/11 – P(A∩B)
⇒ P(A∩B) = 13/11 – 7/11
⇒ P(A∩B) = 6/11
P(A|B) = (6/11) / (6/11).
P(A|B) = 1.
Most Upvoted Answer
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ___...
Understanding the Problem
To find P(A|B), we can use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) is the probability of A given B.
- P(A ∩ B) is the probability of both A and B occurring.
- P(B) is the probability of B.
Given Values
- P(A) = 7/11
- P(B) = 6/11
- P(A ∪ B) = 8/11
Finding P(A ∩ B)
Using the formula for the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
We can rearrange this to find P(A ∩ B):
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Now substituting the provided values:
P(A ∩ B) = (7/11) + (6/11) - (8/11)
Calculating P(A ∩ B)
- Combine the fractions:
P(A ∩ B) = (7 + 6 - 8) / 11
P(A ∩ B) = 5/11
Calculating P(A|B)
Now, substitute P(A ∩ B) and P(B) into the conditional probability formula:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = (5/11) / (6/11)
This simplifies to:
P(A|B) = 5/6
Conclusion
The correct answer is option 'D' (5/6). This indicates that given event B has occurred, the probability of event A occurring is 5/6.
To find P(A|B), we can use the formula for conditional probability:
P(A|B) = P(A ∩ B) / P(B)
Where:
- P(A|B) is the probability of A given B.
- P(A ∩ B) is the probability of both A and B occurring.
- P(B) is the probability of B.
Given Values
- P(A) = 7/11
- P(B) = 6/11
- P(A ∪ B) = 8/11
Finding P(A ∩ B)
Using the formula for the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
We can rearrange this to find P(A ∩ B):
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)
Now substituting the provided values:
P(A ∩ B) = (7/11) + (6/11) - (8/11)
Calculating P(A ∩ B)
- Combine the fractions:
P(A ∩ B) = (7 + 6 - 8) / 11
P(A ∩ B) = 5/11
Calculating P(A|B)
Now, substitute P(A ∩ B) and P(B) into the conditional probability formula:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = (5/11) / (6/11)
This simplifies to:
P(A|B) = 5/6
Conclusion
The correct answer is option 'D' (5/6). This indicates that given event B has occurred, the probability of event A occurring is 5/6.
|
Explore Courses for Civil Engineering (CE) exam
|
|
Similar Civil Engineering (CE) Doubts
Top Courses for Civil Engineering (CE)View all
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer?
Question Description
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer?.
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer?.
Solutions for If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
Download more important topics, notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free.
Here you can find the meaning of If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A|B) = ________a)1b)2/3c)1/2d)5/6Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Civil Engineering (CE) tests.
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup