Question
Download Solution PDFIf A and B are two events such that P(A) ≠ 0 and P(B | A) = 1, then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- \(\rm P(A|B) = \frac {P(A \;∩ \; B)}{P(B)}\)
- \(\rm P(B|A) = \frac {P(A \;∩ \; B)}{P(A)}\)
- 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
⇒ \(\rm P(B|A) = \frac {P(A \;∩ \; B)}{P(A)} = 1\)
⇒ P(A ∩ B) = P(A)
⇒ (A ∩ B) = A
So, every element of A is in B, but B has more elements.
∴ A ⊂ B
Last updated on May 19, 2025
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