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Question
If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.
Options
`1/12`
`3/4`
`1/4`
`3/16`
Solution
If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals `1/4`.
Explanation:
Given that: P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`
`"P"("A"/"B") = ("P"("A" ∩ "B"))/("P"("B"))`
`1/4 = ("P"("A" ∩ "B"))/(1/3)`
⇒ P(A ∩ B) = `1/4 xx 1/3 = 1/12`
Now P(A' ∩ B') = 1 – P(A ∪ B)
= 1 – [P(A) + P(B) – P(A ∩ B)]
= `1 - [1/2 + 1/3 - 1/12]`
= `1 - [5/6 - 1/12]`
= `1 - 9/12`
= `3/12`
= `1/4`
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