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For two events A and B of a sample space S, if P(A) =38, P(B) = 12 and P(A ∪ B) = 58. Find the value of the following: P(A' ∪ B') - Mathematics and Statistics

Sum

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')

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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`.

Concept: Multiplication Theorem on Probability
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