Let A and B be two events such that `P (bar(AuuB))=1/6, P(AnnB)=1/4and P(barA)=1/4,where barA` stands for the complement of the event A. Then the events A and B are

Options

A. mutually exclusive and independent
B. equally likely but not independent
C. Independent but not equally likely
D. independent and equally likely

Answer

C

Explanation

`P (bar(AuuB))=1/6`
`P(AuuB)=5/6,P(A)=3/4`
`P(AuuB)-P(A)+P(B)-P(AnnB)=5/6`
`impliesP(B)=5/6-3/4+1/4=1/3`
`impliesP(AnnB)=P(A).P(B)=1/4`