if A and B are two events such that P(AUB)= 5/6, P(AnB)=1/3, P(B')=1/2 then the events are
(a) dependent
(b) independent
(c) mutually exclusive 
(d) none of these 
( with explanation)

Dear Student,
P(B')  = 12P(B)= 1 - P(B')  =1 - 12= 12P(AB) = P(A) +P(B) - P(AB)P(A) = P(AB) -P(B) + P(AB)=56 - 12 + 13= 5 - 3 + 26= 23P(A|B) = P(AB)P(B)= 1312 = 23 = P(A)

Hence, the events are independent of each other.
Regards,

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