# Chapter 4 - Probability - 4-4 Multiplication Rule: Basics - Basic Skills and Concepts: 18

0.583. The tendency is that the whole batch will be accepted. Hence the scheme is likely to no serve its purpose.

#### Work Step by Step

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.

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