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If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then
- a)B ⊂ A
- b)B = ϕ
- c)A ⊂ B
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...
Concept:
- P(A|B) = P(A∩B)/P(B)
- P(B|A) = P(A∩B)/P(A)
- A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
- ϕ = Empty set = {}
Calculation:
Given: P(B/A) = 1
⇒ P(B|A) = P(A∩B)/P(A) = 1
⇒ P(A ∩ B) = P(A)
⇒ (A ∩ B) = A
So, every element of A is in B, but B has more elements.
∴ A ⊂ B
Most Upvoted Answer
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...
Concept:
- P(A|B) = P(A∩B)/P(B)
- P(B|A) = P(A∩B)/P(A)
- A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
- ϕ = Empty set = {}
Calculation:
Given: P(B/A) = 1
⇒ P(B|A) = P(A∩B)/P(A) = 1
⇒ P(A ∩ B) = P(A)
⇒ (A ∩ B) = A
So, every element of A is in B, but B has more elements.
∴ A ⊂ B
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Community Answer
If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then...
Concept:
- P(A|B) = P(A∩B)/P(B)
- P(B|A) = P(A∩B)/P(A)
- A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
- ϕ = Empty set = {}
Calculation:
Given: P(B/A) = 1
⇒ P(B|A) = P(A∩B)/P(A) = 1
⇒ P(A ∩ B) = P(A)
⇒ (A ∩ B) = A
So, every element of A is in B, but B has more elements.
∴ A ⊂ B
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If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?
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If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer?.
Solutions for If A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, thena)B ⊂ Ab)B = c)A ⊂ Bd)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT.
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