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Sum

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')

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#### 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`

Concept: Addition Theorem of Probability

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