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Question
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
Solution
P(A) = 0.4
P(A ∪ B) = 0.7
Given A and B are independent
⇒ P(A ∩ B) = P(A) . P(B)
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
(i.e.,) 0.7 = 0.4 + P(B) – (0.4)(P(B))
(i.e.,) 0.7 – 0.4 = P(B)(1 – 0.4)
0.3 = P(B) 0.6
⇒ P(B) = `0.3/0.6`
= `3/6`
= 0.5
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