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Question
The probability that at least one of the two events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, evaluate `"P"(bar"A") + "P"(bar"B")`
Solution
We know that,
A ∪ B denotes that atleast one of the events occurs
And A ∩ B denotes that the two events occur simultaneously.
So, P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
⇒ 0.6 = P(A) + P(B) – 0.3
⇒ 0.9 = P(A) + P(B)
⇒ 0.9 = `1 - "P"(bar"A") + 1 - "P"(bar"B")`
⇒ `"P"(bar"A") + "P"(bar"B")` = 2 – 0.9 = 1.1
Hence, the required answer is 1.1
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