.The Arizona State University Statistical Summary provides information on various characteristics of ASU faculty. Data from one year on the variables age and rank of ASU faculty members yielded the contingency table shown below.

RANK

AGE Full Prof, R1 Associate Prof. R2 Assoc Prof R3 intructor R4 Total

Under 30,Y 2 3 57 6 68

30-39,G 52 170 163 17 402

40-49 ,M 156 125 61 6 348

50-59,R 145 68 36 4 253

60 & over ,O 75 15 3 0 93

TOTAL 430 381 320 33 1164

uppose an ASU faculty member is selected at random, answer the following questions, using the letters representing the events:5 points each

a.What is the probability that the member is neither a full professor nor an associate professor?

b.What is the probability that the selected member is an assistant professor or the member is between 40 - 49 years of age?Addition Rule

c.If the selected member is an associate professor, what is the probability that the member is older than 49? (conditional probability)