## Objectives

- To practice with theoretical and experimental probability.
- To practice with independent and dependent events.

## Materials

- Bag that you cannot see through
- Paper
- Marker or Pen
- Scissors

## Pre-Investigation Questions

- How many times do you think you will need to pull a letter from the bag until you get all the letters to spell MATH? Explain your reasoning.
- What is the sample space?
- Are there any outcomes that are equally likely? Explain.

## Procedure

Work on your own or with a friend.

- Use your scissors to cut out $4$4 small pieces of paper.
- On each piece of paper write one letter of the word MATH.
- Place the pieces of paper in the bag.
- Shake up the bag then draw a letter from the it. Record how much of each letter you find by listing the letters and keeping a tally next to them.
- Continue to draw letters until you have gotten all of the letters to spell MATH.

## Post-Questions

- How many total letters did you need to draw from the bag to get all the letters you needed?
- Compare this to your estimate. Is it close?
- If you were to redo the experiment do you think you would need to draw the same number of letters to spell the word? Why or why not?
- Data is always more reliable when you have more of it. Redo the experiment once more and see if you get the same result.
- Is the action of drawing a letter from the bag an independent or dependent event? Explain.

##### Work with a friend!

- Did they have the same original estimate as you? If not how is it different?
- Compare and contrast the results you got, then take the average of your results.
- Is the average of your numbers close to either of your estimates?
- Compare this to how close your data was to your estimate on its own.

## OPTIONAL

Try it with your own word!

- Write down a word largely and cut out each of the letters separately.
- Make a prediction as to how many letters you will need to draw from the bag before the word is spelled.
- Place the letters in the bag and keep a tally of how many times you draw each letter from the bag before you get everything you need to spell the word.
- Compare it to your prediction.
- Compare it to the amount of letters that had to be drawn to spell MATH.