We didn’t cover these concepts in detail in class, but we will need them to discuss “events” in probability (and they come up on HW#3, and may come up on the exam tomorrow!):
As a quick review, recall that for a given probability experiment, the sample space S is the set of all possible outcomes, and an event is any particular set of outcomes (i.e., a “subset” of S)
For any sets (i..e, events) A and B, we can look at the union of A and B and the intersection of A and B:
The union of A & B (notation: A ⋃ B) means you combine the elements of A & B, i.e., elements that are in A or B. So for For Sec 4.2 #7, where B = {4,6} and C = {1,4}, the union is B ⋃ C = {1,4,6} (all the elements that are in one set or the other!)
Also, the intersection of A & B (notation: A ⋂ B) means you take the elements that are in both A and B. So for B = {4,6} and C = {1,4}, the intersection is B ⋂ C = {4} (since 4 is the only element that’s in both sets)
There’s also the complement of a set A (notation: A^C), which means everything that’s not in the given set. Since we are always looking at an event A ⊆S, the complement of A means all the elements of S that are not in A (sometimes also denoted by S – A).
So in the exercise where the sample space is S = {1,2,3,4,5,6}, and for the given event B = {4,6}, the complement of B is {1,2,3,5}.
