Question 1170936
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