The probability that at least one of the events A and B occur is 0.6. If A and B occurs simultaneously with probability 0.2, then P(A') + P(B') is

Engineering

Mathematics

Conditional Probability

Question

0.8

1.2

1.4

None of these

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Given, P(A⋃B) = 0.6, P(A∩B) = 0.2

P(A') + P(B') – P(A∩B) =P(A⋃B)

⇒ P(A') + P(B') – 0.2 = 0.6 [∵ P(A∩B) = 0.2]

⇒ P(A') + P(B') = 0.8

⇒ [1 – P(A')] + 1 – P(B') = 0.8 [∵ P(X) = 1 – P(X')]

⇒ 2 – [P(A') + P(B')] = 0.8

⇒ – [P(A')+P(B')] = 0.8 – 2

⇒ P(A') + P(B') =1.2

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