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Probability with words (Investigation)



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


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

Pre-Investigation Questions

  1. 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.
  2. What is the sample space?
  3. Are there any outcomes that are equally likely? Explain.


Work on your own or with a friend.

  1. Use your scissors to cut out $4$4 small pieces of paper.
  2. On each piece of paper write one letter of the word MATH.
  3. Place the pieces of paper in the bag.
  4. 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.
  5. Continue to draw letters until you have gotten all of the letters to spell MATH.


  1. How many total letters did you need to draw from the bag to get all the letters you needed?
  2. Compare this to your estimate. Is it close?
  3. 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?
  4. Data is always more reliable when you have more of it. Redo the experiment once more and see if you get the same result.
  5. Is the action of drawing a letter from the bag an independent or dependent event? Explain.
Work with a friend!
  1. Did they have the same original estimate as you? If not how is it different?
  2. Compare and contrast the results you got, then take the average of your results.
  3. Is the average of your numbers close to either of your estimates?
  4. Compare this to how close your data was to your estimate on its own.


Try it with your own word!

  1. Write down a word largely and cut out each of the letters separately. 
  2. Make a prediction as to how many letters you will need to draw from the bag before the word is spelled. 
  3. 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. 
  4. Compare it to your prediction. 
  5. Compare it to the amount of letters that had to be drawn to spell MATH.



Calculate probabilities, using fractions, percentages, and ratios

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