Advanced Sample Spaces

Focus Questions:

• How can we analyze compound events in a more efficient way?
• What effect does replacement have on probability

Do Now:

To win this game, you must pick a green marble out of each bucket.  What is the probability of winning this game? Use a sample space to show your work.

Part 1: A Question of Replacement

In this part of the lesson, we will explore what effect replacing the first block chosen from a bag has on the probability of getting a matching pair of red blocks.  Here is what you will need:

• A bag with four blocks - 2 RED, 1 BLUE, and 1 YELLOW

Game #1:

• Pick 1 block from the bag, put it back in the bag, and then draw a second block.
• If both blocks are RED - you win.
• Repeat this 20 times and record how many times you win.

Game #2:

• Pick 1 block from the bag, do NOT put it back in the bag, and then draw a second block.
• If both blocks are RED - you win.
• Repeat this 20 times and record how many times you win.

Record your results in this form.

Part 2: Advanced Sample Spaces

In this part of the lesson, we will look at how we can use a more advanced form of tables and tree diagrams to help us analyze a greater variety of events with more efficiency.  Here is what you will need to do:

• Create a SAMPLE SPACE to show all of the outcomes for both experiment #1 and experiment #2.  Be careful with experiment #2 - it is tricky.

NOTE TAKING - What we want to do is be able to use a more efficient version of our sample spaces that focuses on the relative frequency of each different type of outcome as opposed to representing each "equally likely" outcome.  We will try some of these together as a class.  Here is an example of a more advanced "table" and a more advanced "tree diagram":

Part 3: Making Money

In this part of the money we will begin to take a look at how to decide whether a game will make money at a carnival. We will continue to explore this next class.

Here is another version of making purple. Do you expect the school to make money playing this game? Justify your answer.

Here is what you MUST do before next class:

• ACE (1-4, 8)