SOLUTION: 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 st

Question 1170936: 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? (D) is not involved in Greek life?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to calculate the probabilities:
**1. Calculate the percentage of Arts & Humanities students:**
* Total percentage of STEM and Social Sciences students: 20% + 45% = 65%
* Percentage of Arts & Humanities students: 100% - 65% = 35%
**2. Calculate the probabilities:**
* **(A) Probability of studying Arts & Humanities:**
* 35% or 0.35
* **(B) Probability of studying STEM and NOT involved in Greek life:**
* Percentage of STEM students not in Greek life: 100% - 15% = 85%
* Probability: 20% * 85% = 17% or 0.17
* **(C) Probability of studying Arts & Humanities and NOT involved in Greek life:**
* Probability: 35% * 35% = 12.25% or 0.1225
* **(D) Probability of studying Social Sciences and NOT involved in Greek life:**
* Percentage of Social Science students not in Greek life: 100% - 40% = 60%
* Probability: 45% * 60% = 27% or 0.27
* **(E) Probability of being involved in Greek life:**
* Probability: (20% * 15%) + (45% * 40%) + (35% * 65%) = 3% + 18% + 22.75% = 43.75% or 0.4375
* **(F) Probability of NOT being involved in Greek life:**
* Probability: 100% - 43.75% = 56.25% or 0.5625

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