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Question
For two events A and B of a sample space S, if P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`. Find the value of the following: P(A' ∪ B')
Solution
It is given that,
P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
∴ `5/8 = 3/8 + 1/2 - "P"("A" ∩ "B")`
∴ P(A ∩ B) = `3/8 + 1/2 - 5/8` = `2/8` = `1/4`
P(A' ∪ B') = P[(A ∩ B)']
= 1 – P(A ∩ B)
= `1 - 1/4`
= `3/4`.
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