## Elementary Statistics (12th Edition)

Events are dependent, if the outcome of one effects the outcome of the other. Here the events are dependent, because the sampling was done without replacement. $P(A \cap B)=P(A)\cdot P(B|A)$. Hence $P(A \cap B)=\frac{708}{810}\cdot\frac{707}{809}\cdot\frac{706}{808}\cdot\frac{705}{807}=0.583>0.05.$ The tendency is that the whole batch will be accepted. Hence the scheme is likely to no serve its purpose.