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Sum

The probability that atleast one of A and B occur is 0.6. If A and B occur simultaneously with probability 0.2, then find `"P"(bar"A") + "P"(bar"B")`

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#### Solution

Here P(A ∪ B) = 0.6, P(A ∩ B) = 0.2

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

0.6 = P(A) + P(B) – 0.2

P(A) + P(B) = 0.8

`"P"(bar"A") + "P"(bar"B")` = 1 – P(A) + 1 – P(B)

= 2 – [P(A) + P(B)]

= 2 – 0.8

= 1.2

Concept: Algebra of Events

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