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if `A` and `B` be two events such that `P(A)=1/4, P(B)=1/3` and `P(AuuB)=1/2,` show that `A` and `B` are independent events. Select the correct answer from above options

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For independent events `A` and `B`, `P(AnnB) = P(A)P(B)`. Also, `P(AuuB) = P(A)+P(B)-P(AnnB)` Putting the given values, `1/2 = 1/4+1/3 -P(AnnB)` `1/2 = 7/12 - P(AnnB)` `=>P(AnnB) = 7/12 - 1/2 = 1/12` `=>P(AnnB) = 1/4**1/3 = P(A)P(B)` Thus, `A` and `B` are independent events.

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