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Events A and B are such that P(A)=1//2,P...

Events A and B are such that `P(A)=1//2,P(B)=7//12,` and P (not A or not B) = 1/4. State whether A and B are independent ?

Text Solution

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If A and B are mutually exclusive
P (not A or not B) = `1/4` i.e.
By substituting the values
`P (A ∩ B) = 1 – 1/4 = 3/4 …… (1)`
For two mutually exclusive events
`P (A ∩ B) = 0` but here `P (A ∩ B) ≠ 0`
Hence, A and B are not mutually exclusive.
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