Question

4. At a certain university, students can choose one of 3 general areas of study. Twenty percent of the students are studying STEM, 45% are studying Social Sciences and the rest are studying Arts & Humanities. In addition, 15% of the STEM students and 40% of the Social Science students are involved in Greek life (in a sorority or fraternity). Only 35% of the Arts and Humanities students are NOT members of a sorority or fraternity. (***Similar to example 4***)What is the probability that a student....(a) studies Arts & Humanities? (b) studies STEM and is NOT involved in Greek life? (c) studies Arts & Humanities and is NOT involved in Greek life? (d) studies Social Sciences and is NOT involved in Greek life? (e) is involved in Greek life? (f) is not involved in Greek life?

Answer 1

$100-20-45=35(\%)$

a) $P(Arts\ \&\ Humanities )=0.35$

b) $P(STEM\ and\ not\ involved\ in \ Greek\ life)$

$=0.2\cdot(1-0.15)=0.17$

c) $P(Arts\ \&\ Humanities\ and\ not\ involved\ in \ Greek\ life)$

$=0.35\cdot0.35=0.1225$

d) $P(Social \ Sciences\ and\ not\ involved\ in \ Greek\ life)$

$=0.45\cdot(1-0.40)=0.27$

e) $P(involved\ in \ Greek\ life)$

$=1-(0.17+0.1225+0.27)=0.4375$

f) $P(not\ involved\ in \ Greek\ life)$

$=0.17+0.1225+0.27=0.5625$