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in Introduction to Probability Theory by (49.1k points)
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If P(A) = 0.4, P(B) = 0.7 and P(B/A) = 0.5, find P(A/B) and P(A ∪ B).

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P(B/A) = 0.5 

⇒ P(B ∩ A)/P(A) = 0.5 

(i.e.,) P(B ∩ A)/0.4 = 0.5 

∴ P(B ∩ A) = 0.4 × 0.5 = 0.2 

(i.e.,) P(A ∩ B) = 0.2 

P(A ∪ B)= P(A) + P(B) – P(A ∩ B) 

P(A ∪ B) = 0.4 + 0.7 – 0.2 = 0.9 

P(A/B) = P(A ∩ B)/P(B) = 0.2/0.7 = 2/7

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