Questions: The following contingency table cross-classifies medical school faculty by the characteristics gender and rank. P(R3) = 0.403 b. Find P(R3 G1). P(R3 G1) = 0.367 c. Are events G1 and R3 independent? A. No. Events G1 and R3 are only independent if P(R3) ≠ P(R3 G1). B. No. Events G1 and R3 are only independent if P(R3) = P(R3 G1). C. Yes. Events G1 and R3 are independent because P(R3) = P(R3 G1). D. Yes. Events G1 and R3 are independent because P(R3) ≠ P(R3 G1). Medical school faculty gender and rank Rank veriver Male G1 Female G2 Total --------------- Professor R1 21,340 3,446 24,786 Associate professor R2 16,299 5,278 21,577 Assistant professor R3 25,502 14,045 39,547 Instructor R4 5,521 5,027 10,548 Other R5 767 849 1,616 Total 69,429 28,645 98,074

Transcript text: The following contingency table cross-classifies medical school faculty by the characteristics gender and rank. \[ \mathrm{P}\left(\mathrm{R}_{3}\right)=0.403 \] b. Find $P\left(R_{3} \mid G_{1}\right)$. \[ P\left(R_{3} \mid G_{1}\right)=0.367 \] c. Are events $G_{1}$ and $R_{3}$ independent? A. No. Events $G_{1}$ and $R_{3}$ are only independent if $P\left(R_{3}\right) \neq P\left(R_{3} \mid G_{1}\right)$. B. No. Events $G_{1}$ and $R_{3}$ are only independent if $P\left(R_{3}\right)=P\left(R_{3} \mid G_{1}\right)$. C. Yes. Events $G_{1}$ and $R_{3}$ are independent because $P\left(R_{3}\right)=P\left(R_{3} \mid G_{1}\right)$. D. Yes. Events $G_{1}$ and $R_{3}$ are independent because $P\left(R_{3}\right) \neq P\left(R_{3} \mid G_{1}\right)$. Medical school faculty gender and rank \begin{tabular}{|c|c|c|c|c|} \hline \multirow{8}{*}{Rank} & \multicolumn{4}{|c|}{veriver} \\ \hline & & \[ \begin{array}{c} \text { Male } \\ G_{1} \end{array} \] & Female $\mathrm{G}_{2}$ & Total \\ \hline & \[ \begin{array}{l} \text { Professor } \\ \mathbf{R}_{\mathbf{1}} \end{array} \] & 21,340 & 3,446 & 24,786 \\ \hline & Associate professor $R_{2}$ & 16,299 & 5,278 & 21,577 \\ \hline & Assistant professor $R_{3}$ & 25,502 & 14,045 & 39,547 \\ \hline & \[ \begin{array}{l} \text { Instructor } \\ \mathbf{R}_{\mathbf{4}} \end{array} \] & 5,521 & 5,027 & 10,548 \\ \hline & Other $\mathrm{R}_{5}$ & 767 & 849 & 1,616 \\ \hline & Total & 69,429 & 28,645 & 98,074 \\ \hline \end{tabular}