The Clemson University Fact Book for 2007 shows that 123 of

The Clemson University Fact Book for 2007 shows that 123 of the university\'s 338 assistant professors were women, along with 76 of the 263 associate professors and 73 of the 375 full professors.

A.	What is the probability that a randomly chosen Clemson professor of any rank is a woman? Give your answer to 4 decimal places. Fill in the blank:

The Clemson University Fact Book for 2007 shows that 123 of the university\'s 338 assistant professors were women, along with 76 of the 263 associate professors and 73 of the 375 full professors. What is the probability that a randomly chosen Clemson professor of any rank is a woman? What is the conditional probability that a randomly chosen professor is a woman, given that the person chosen is a full professor?

Solution

a) What is the probability that a randomly chosen Clemson professor is a woman?
b) What is the conditional probability that a randomly chosen professor is a woman, given that the person chosen is a full professer?
c) Are the rank and gender of Clemson professors independent? How do you know?

.............................. men ............... women .......... total
asstt. prof ............ 215 .................123 ............... 338
associate prof .... 187 ..................76 ................. 263
full professor ....... 302 ................. 73 ................. 375
total ...................... 704 ................. 272 ............... 976

a. 272/976
b. 73/375
c. no P[woman | rank] is different for different ranks