1. Chapter 3.1 Probability
Students will learn several ways to model situations involving probability, such as tree diagrams and area models. They will formalize methods for computing probabilities of unions, intersections and complements of events. Then they will calculate expected value in games of chance.

2. 3.1.1 Using an Area Model

3. Likelihood something will happen
Probability
Likelihood something will happen
Can’t be negative because we can’t have a negative number or outcomes or want a negative amount of something to happen
Probability: The likelihood that an event will occur
Written as a ratio, decimal or percent
An event that is certain to happen has a probability of 1
An event that has no chance of happening has a probability of 0

4. Terms we need to know for Probability
Event: any outcome or set of outcomes from a situation, anything that could happen in that situation Rolling a 5 is an event Successful Event: set of all outcomes that are of interest in a given situation, what you want to happen If you win when you roll an even number then {2,4,6} would be successful events Sample Space: all possible outcomes Roll a dies {1,2,3,4,5,6} This is just a list of all the outcomes not the probability for them

5. Theoretical Probability
Using the math to find the probability
When the outcomes in the sample space of an experiment have the same chance of occurring, the outcomes are equally likely
Idea is what you want to happen in numerator/how many things could happen

6. Example
A bag of marbles contains 8 yellow, 2 red, and 10 green marbles. An experiment consists of selecting one marble at random from the bag. Find the theoretical probability of each outcome.
Selecting a yellow marble
Selecting a red or a yellow marble

7. Experimental Probability
An experiment is an activity involving chance Use the data from doing the experiment to determine the probability Number of times event occurs number of trials

8. Example
An experiment consists of randomly selecting marbles from a bag. Use the results in the table to find the experimental probability of each event.
Select a green marble
Not selecting a white

9. Area Model
When multiple events are happening, starting with 2 Similar to box method for multiplying binomials Top is one of the outcomes with probability for it to happen or not Side is the other outcome with probability for it to happen or not The Area model then represents all the combinations and probabilities for each to happen

10. Area Model examples
Pg 145 read through 3-1 as a group and work through a, b and c a – fill in table b – check probabilities c – what if probability of each event is different

11. More examples
How would you set up the table for 3-3 What about 3-4 Try 3-6 Roll and Win

12. Using a Tree Diagram

13. Tree Diagram
Using the roots of a tree or tree branches to give you all the paths and possible outcomes in a given situation Each branch is a different possible event End of the branches give you all the outcomes, where sample space could be found Multiply along the path (similar to finding the boxes) Add all results at the ends of the branches together and you should get 1 Works better for dependent probability I like this it seems more visual to me

14. Independent Probability
If the occurrence of one event does not affect the probability of the other If A and B are independent events then P(A and B)=P(A) * P(B) Rolling a die and flipping a coin Pick a card replacing it and then picking another card If two or more events are independent then multiply their individual probabilities

15. Dependent Probability
If the occurrence of one event does affect the probability of the other If A and B are dependent events then P(A and B) = P(A)*P(B after A) In other words the second probability changes as a result of the first Outcomes goes down by 1 and numerator could change depending on the event You have a situation where you do not replace something Pick a marble, not replacing it and then picking another marble

16. Determine if Independent or Dependent
A die is rolled two times.
The numbers 1-20 are written on pieces of paper and put in a box. Two pieces are randomly selected and not replaced.
Selecting a marble and replacing it
Selecting a marble and not replacing it
Selecting two boys from this class to do an errand

17. 3-12
Looking at 3-12 on page 150 Then continue onto 3-13 Could you make an area model for this Otherwise look at it like a tree First set of branches is spinner 1 Second set of branches is spinner 2 Write the probability along each branch

18. 3-14
Set up a probability tree for this situation

19. Homework
Pg and 3-18 Wkst