## Elementary Statistics (12th Edition)

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 $P(A \cap B)=\frac{6}{1000}\cdot\frac{6}{1000}\cdot\frac{6}{1000}=\frac{216}{1,000,000,000}<0.05.$ Hence it is unlikely. b) 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 $P(A \cap B)=\frac{6}{1000}\cdot\frac{5}{999}\cdot\frac{4}{998}=\frac{120}{998,001,000}<0.05.$ Hence it is unlikely.