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Question
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
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Solution
Given A and B are independent.
⇒ P(A ∪ B) = P(A) . P(B)
Here P(A ∪ B) = 0.6 and P(A) = 0.2
To find P(B):
Now, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
(i.e.,) P(A ∪ B) = P(A) + P(B) – P(A) . P(B)
(i.e.,) 0.6 = 0.2 + P(B) (1 – 0.2)
P(B) (0.8) = 0.4
⇒ P(B) = `0.4/0.8`
= `4/8`
= `1/2`
= 0.5
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