Question

Use the Data Table to answer the question Are Year and technology class enrollment dependent or independent? Explain

Answer 1

Two events R and S are said to be independent if the occurence of R Makes it neither more nor less probable that S occurs and , conversely, if the occurrence of R makes it neither more nor less prbable that R occurs.

This implies that if; P(Sophomore|Robotics)= P(Sophomore), then they and independent, conversly if they are not equal, they are dependent.

`\begin{gathered} p(sophomore|robotics)=(p(S\cap R))/(p(R))=((18)/(76))/((39)/(76)) \\ =(18)/(39)=(6)/(13) \\ P(sophomore)=(38)/(76)=(1)/(2) \\ \sin ce, \\ p\mleft(sophomore|robotics\mright)\\e P(sophomore) \\ \text{Therefore they are dependent because }p(sophomore|robotics)=(6)/(13)\\e P(sophomore)=(1)/(2) \end{gathered}`