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Question
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is ______.
Options
0.4
0.8
1.2
1.6
Solution
The probability that at least one of the events A and B occurs is 0.6. If A and B occur simultaneously with probability 0.2, then `P(barA) + P(barB)` is 1.2.
Explanation:
Given that: 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) = 0.6 + 0.2 = 0.8
And `1 - P(barA) + 1 - P(barB)` = 0.8
⇒ `P(barA) + P(barB)` = 2 – 0.8 = 1.2
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