1.

Let A and B be the events 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 (i) mutually exclusive, (ii) independent.

Answer» Correct Answer - (i) No (ii) No
P (not A or not B) `=P (bar(A) or bar(B))=P( bar(A) uu bar(B))`
`=P (bar(A nn B))=1- P (A nn B)`
`implies 1-P (A nn B)=1/4 implies P(A nn B)=3/4`.
(i) Since `P(A nn B) ne 0`, so A and B are not mutually exclusive.
(ii) `P(A)xxP(B)=(1/2xx7/12)=7/24 ne P(A nn B)`
`implies` A and B are not independent.


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