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Question
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find
- P(A ∩ B)
- P(A|B)
- P(A ∪ B)
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Solution
(i) Given P(B|A) = 0.4
⇒ `(P (A cap B))/(P(A)) = 0.4`
⇒ P(A ∩ B) = P (A) × 0.4
= 0.8 × 0.4
= 0.32
(ii) `P(A|B) = (P (AcapB))/(P(B))`
`= 0.32/0.5`
= 0.64
(iii) P(A ∪ B) = P (A) + P (B) - P (A ∩ B)
= 0.8 + 0.5 - 0.32
= 1.3 - 0.32
= 0.98
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