Chapter 4 - Probability and Counting Rules - 4-3 The Multiplication Rules and Conditional Probability - Extending the Concepts - Page 226: 53

No, unless P(A)=0 or P(B)=0

Since A and B are two mutually exclusive events, we have P(A and B)=0 For A and B to be independent events, we need P(A and B)=P(A)*P(B) this requires that either P(A)=0 or P(B)=0 The conclusion is that A and B will not be independent events unless at least one of the individual probability is zero.