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Question
Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals ______.
Options
`1/10`
`3/10`
`3/8`
`6/7`
Solution
Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals `3/8`.
Explanation:
P(A ∩ B) = P(A|B) P(B)
= 0.5 × 0.2
= 0.1
P(A′|B′) = `("P"("A'" ∩ "B'"))/("P"("B'"))`
= `("P"[("A" ∪ "B")])/("P"("B'"))`
= `(1 - "P"("A" ∪ "B"))/(1 - "P"("B"))`
= `(1 - "P"("A") - "P"("B") + "P"("A" ∩ "B"))/(1 - 0.2)`
= `3/8`.
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