Answer
a) Not unlikely.
b)Not unlikely.
Work Step by Step
a) Events are dependent, if the outcome of one effects the outcome of the other. Here the events are independent, because the sampling was done with replacement, hence here $P(B|A)=P(B)$. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{904}{1000}\cdot\frac{904}{1000}\cdot\frac{904}{1000}=\frac{738,763,264}{1,000,000,000}>0.738>0.05.$ Hence it is not unlikely.
b) Two events are dependent, if the outcome of one effects the outcome of the other. Here the events are dependent, because the sampling was done with out. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{904}{1000}\cdot\frac{903}{999}\cdot\frac{902}{998}=\frac{736,313,424}{997,002,000}>0.738>0.05.$ Hence it is not unlikely.
