UPSC Exam > UPSC Questions > P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersec...
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P(A) = 1/2
P(B) = 5/8
P(AUB) = 3/4
P(A intersection B ) = ???
answer is 1/4 ..how can it be ?
P(B) = 5/8
P(AUB) = 3/4
P(A intersection B ) = ???
answer is 1/4 ..how can it be ?
Most Upvoted Answer
P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1...
Understanding the Problem
Given:
- P(A) = 1/2
- P(B) = 5/8
- P(A U B) = 3/4
We need to find P(A ∩ B).
Using the Inclusion-Exclusion Principle
To find P(A ∩ B), we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Given values:
- P(A) = 1/2
- P(B) = 5/8
- P(A U B) = 3/4
Substitute the values into the formula:
3/4 = 1/2 + 5/8 - P(A ∩ B)
Solving for P(A ∩ B)
Now, solve for P(A ∩ B):
3/4 = 4/8 + 5/8 - P(A ∩ B)
3/4 = 9/8 - P(A ∩ B)
P(A ∩ B) = 9/8 - 3/4
P(A ∩ B) = 9/8 - 6/8
P(A ∩ B) = 3/8
Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 3/8, not 1/4 as initially stated.
Given:
- P(A) = 1/2
- P(B) = 5/8
- P(A U B) = 3/4
We need to find P(A ∩ B).
Using the Inclusion-Exclusion Principle
To find P(A ∩ B), we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Given values:
- P(A) = 1/2
- P(B) = 5/8
- P(A U B) = 3/4
Substitute the values into the formula:
3/4 = 1/2 + 5/8 - P(A ∩ B)
Solving for P(A ∩ B)
Now, solve for P(A ∩ B):
3/4 = 4/8 + 5/8 - P(A ∩ B)
3/4 = 9/8 - P(A ∩ B)
P(A ∩ B) = 9/8 - 3/4
P(A ∩ B) = 9/8 - 6/8
P(A ∩ B) = 3/8
Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 3/8, not 1/4 as initially stated.
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P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ?
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P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ?.
P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P(A) = 1/2 P(B) = 5/8P(AUB) = 3/4P(A intersection B ) = ???answer is 1/4 ..how can it be ?.
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