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Question
If `P(A) = 6/11, P(B) = 5/11 "and" P(A ∪ B) = 7/11` find
- P(A ∩ B)
- P(A|B)
- P(B|A)
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Solution
(i) Now, P(A) + P(B) - P(A ∩ B)= `7/11`
⇒ P(A ∩ B) = `6/11 + 5/11 - 7/11`
`= 4/11`
(ii) `P(A|B) = (P(A ∩ B))/(P(B))`
`= (4/11)/(5/11)`
`= 4/5`
(iii) `P (B|A) = (P(A ∩ B))/(P (A))`
`= (4/11)/(6/11)`
`= 4/6`
`= 2/3`
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