Fill in the blanks in the following question: If A and B are such that , then P(A') + P(B') = ..................

Question

Philoid · Accepted Answer

10/9

P(A’ ∪ B’) = P(A’) + P(B’) – P(A’ ∩ B’) {using union of two sets}

⇒ P(A’) + P(B’) = P(A’ ∪ B’) + P(A’ ∩ B’)

∵ P(A’ ∩ B’) = P(A ∪ B)’ {using De Morgan’s law}

⇒ P(A’ ∩ B’) = 1- P(A ∪ B) = 1 – 5/9 = 4/9

∴ P(A’) + P(B’) = 2/3 + 4/9 = 10/9