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Question
A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals ______.
Options
`2/3`
`1/2`
`3/10`
`1/5`
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Solution
A and B are events such that P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5. Then P(B′ ∩ A) equals `1/5`.
Explanation:
Given that: P(A) = 0.4, P(B) = 0.3 and P(A ∪ B) = 0.5
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.5 = 0.4 + 0.3 – P(A ∩ B)
P(A ∩ B) = 0.4 + 0.3 – 0.5 = 0.2
∴ P(B' ∩ A) = P(A) – P(A ∩ B)
= 0.4 – 0.2
= 0.2
= `1/5`
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