Probability & Statistics (7 of 62) Union and Intersection - Another Look By Michel van Biezen

Summary:

1. Introduction:

   • The lecturer revisits the concepts of union and intersection to provide a better understanding.

2. Sample Space and Events:

   • Presented is a sample space with numbers 1 through 8.
   • Two events are defined: Event A includes numbers 1, 2, 3, 4, and Event B includes numbers 3, 4, 5, 6.
   • Notable is that both A and B are subsets of the sample space, and they share common elements (3 and 4).

3. Union (A ∪ B):

   • Union can be thought of as "or."
   • All elements belonging to either A or B are included in the union.
   • Elements from A (1, 2), common elements (3, 4), and elements from B (5, 6) are all part of A union B.
   • Thus, A union B contains the elements 1, 2, 3, 4, 5, and 6.

4. Intersection (A ∩ B):

   • Intersection can be thought of as "and."
   • Only elements belonging to both A and B are included in the intersection.
   • The common elements shared by A and B are 3 and 4.
   • Therefore, A intersection B contains only the elements 3 and 4, as they belong to both A and B.

5. Conclusion:

   • The lecturer emphasizes the distinction between union and intersection.
   • Union includes all elements from either A or B, while intersection includes only elements common to both A and B.
   • Using logical terms like "or" and "and" can aid in understanding the concepts of union and intersection, respectively.

Overall, the lecture provides a clear explanation of union and intersection using a sample space and two events, elucidating their meanings and differences effectively.