6. (12 points) Let U be the set of all numbers and let S be the set of factors of the number 12. Fill in the blank with one of the following symbols: E, $, S,Z (a) S_U (d) {2,6, 12} S (b) 3 S (e) {2,6, 7} S (c) 3 U 7. (16 points) The following two-way table cross-classifies medical school faculty by the characteristics gender and rank. Use the table to answer the following. Gender Male Female Total Professor R 21.056 3.058 24,114 Associate professor 16,285 5,166 21,451 R2 Assistant Rank professor 25,746 14,028 39,772 Instructor RA 5.794 5.287 11,081 Other 1676 765 1,441 Total 69.557 28,302 197,859 Write answers as fractions and decimals (Round your answer to the thousandth place). (a) P(GI) (b) P(GIRI) (c) P(G1 or R1) (d) Are the events Ri and G1 independent? Justify your answer with a calculation