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

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 ?

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The correct Answer is:
Not independent
It is given that `P(A)-1/2,P(B)=7/2,andP("not A or not B")=1/4`
`= P(A'uuB')=1/4`
`impliesP((AnnB)')=1/4" "[becauseA'uuB'=(AnnB']`
`impliesa-P(AnnB)=1/4`
or `P(AnnB)=3/4" "(1)`
However `P(A).P(B)=1/2xx7/12=7/24" "(2)`
Here, `3/4ne7/24`
`thereforeP(AnnB)neP(A).P(B)`
Therefore, A and B are not independent events.
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