1. Lesson 11.2 Concept: Comparing Events as Disjoint or Overlapping. Two events are Disjoint if they have no outcomes in common. Two events are Overlapping is they have one or more outcomes in common. Guidelines: Events are set of outcomes. Venn diagrams can be used to show how events are related.

2. Event A Event B Event AEvent B Disjoint Events Overlapping Events

3. A A A A B B B B The sets have no elements in common. The sets have at least one element in common. All elements in B are also in A. All elements in A are also in B.

4. You randomly choose a whole number from 1 through 10. Tell whether the events are disjoint or overlapping. Event A: The number is less than 5. Event B: The number is even. Create a Venn diagram to show the relationship between the events. Event Event A Event B 1 2 3 4 5 6 7 8 9 10 Answer: The numbers 2 and 4 are both less than 5 and even numbers. So, the events are overlapping

5. Two events are independent is the occurrence of one does not affect the likelihood that the other will occur. Two events are dependent is the occurrence of one does affect the likelihood that the other will occur. Tell whether the statement seems to describe independent or dependent events. Each week you and your brother assign chores by writing the chores on pieces of paper and randomly drawing them out of a hat. Event A: You draw “take the trash out” the first week of January. Event B: You draw “take the trash out” the second week of January Solution: Each week your chances of getting “take out the trash” are the same, regardless of whether or not you took the trash out the week before. The events are independent.

6. Two events are independent is the occurrence of one does not affect the likelihood that the other will occur. Two events are dependent is the occurrence of one does affect the likelihood that the other will occur. Tell whether the statement seems to describe independent or dependent events. You have several covered textbooks in your desk that look identical. You pull the books out one at a time and put them in your backpack. Event A: The first book you pull out is your history book. Event B: The second book you pull out is your math book. Solution: Pulling your history book out first decreases the total number of books in your desk. This increases your chances of pulling out your math book next. The events are dependent.