Math 105

Please choose one of the following topics as your main topic 

(1) Mimi made a random guess at 10 true-or-false questions. Let event A be she got at least 6 correct answers. What is the complement of event A? Please explain your answer.

(2) Assume A is an event. Find P(A OR the complement of A), and P(A AND the complement of A). Please explain your result. 

(3) If event A and event B are disjoint, find P(A OR B), and P(A AND B). Please explain your result.

(4) In calculating combination and permutation, we have to leverage factorials. For example, 5! = 5*4*3*2*1=120, 4! = 4*3*2*1=24, 3! = 3*2*1=6, 2! = 2*1, and 1! = 1. What is 0!? Why?