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Question
If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals ______.
Options
`3/10`
`1/5`
`1/2`
`3/5`
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Solution
If A and B are two events such that P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`, then P(A) equals `1/2`.
Explanation:
Given that: P(B) = `3/5`, P(A|B) = `1/2` and P(A ∪ B) = `4/5`
We know that P(A|B) = `("P"("A" ∩ "B"))/("P"("B"))`
⇒ `1/2 = ("P"("A" ∩ "B"))/(3/5)`
∴ P(A ∩ B) = `3/10`
Now P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
`4/5 = "P"("A") + 3/5 - 3/10`
⇒ P(A) = `4/5 - 3/5 + 3/10`
= `1/5 + 3/10`
= `5/10`
= `1/2`
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