\textbf{P(A) = 0.34, P(A ∪ B) = 0.71 =~ P(A) + P(B) -- P(A ∩ B)}  \textbf{(A) If A and B are mutually exclusive, P(A ∩ B) = 0. Then, P(A ∪ B) = P(A) + P(B) which is 0.71= 0.34+P(B). So P(B) = 0.37.}  \textbf{(B) If A and B is independent, P(A ∩ B) = P(A)*P(B). Then, P(A ∪ B) =~ P(A) + P(B) --~ P(A)*P(B) which 0.71 = 0.34 + P(B) - 0.34*P(B). So P(B) = 0.561}  \textbf{(C) P(A ∪ B) = P(A) + P(B) -- P(A ∩ B). We have to know it is mutually exclusive or independent in order to know P(A ∩ B).}  \textbf{(D) If A and B is independent, P(A ∩ B) = P(A)*P(B) =0.34*0.561=0.191}  \textbf{(E) P(A \textbar{} B)=P(A∩B)P(B) = 0} 
\textbf{If P(A) = 0.34 and P(A or B) = 0.71, which of the following is false?} 
Options:
\textbf{P(B) = 0.37 , if A and B are mutually exclusive.} 
\textbf{P(B) = 0.561, if A and B are independent.} 
\textbf{P(B) cannot be determined if A and B are neither mutually exclusive nor independent.} 
\textbf{P(A and B) = 0.191 , if A and B are independent.} 
\textbf{P(A\textbar B) = 0.34 , if A and B are mutually exclusive.} 