# Chapter 4 - Probability - 4-4 Multiplication Rule: Basics - Basic Skills and Concepts: 13

a) Unlikely. b)Unlikely.

#### Work Step by Step

a) Two 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 $P(A \cap B)=\frac{90}{1000}\cdot\frac{90}{1000}=\frac{8100}{1,000,000}=0.0081<0.05.$ Hence it is 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 $P(A \cap B)=\frac{90}{1000}\cdot\frac{89}{999}=\frac{8010}{999,000}=0.00802<0.05.$ Hence it is unlikely.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.