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Question
If P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2` Find the value of the following probability: P(A' ∪ B')
Solution
Here, P(A) = `1/4`, P(B) = `2/5` and P(A ∪ B) = `1/2`
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
∴ P(A ∩ B) = P(A) + P(B) − P(A ∪ B)
= `1/4+2/5-1/2`
= `3/20`
P(A' ∪ B') = P(A ∩ B)` ...[De Morgan's law]
= 1 – P(A ∩ B)
= `1 - 3/20`
= `17/20`
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