Introduction
Today you will travel through a series of stations to discover the chances or odds of something happening. Some stations have virtual simulators that you may use instead of the manipulatives provided at each station. You may choose to work alone through the stations or with a parter and share the data you collect. You must answer the questions independently. Record all of your data in your math journal for future reference.
Task
Station A-Coin Toss
- If I toss a coin, what are the possible outcomes? What is the probability of each outcome? Label these your theoretical probabilities.
- Toss the coin 10 times, record the results of each outcome.
- Toss the coin another 40 times, record the results of each outcome.
- Label the data from 2-3 your experimental probabilities.
- Did the experimental probability from 10 tosses to 50 change the probability of each outcome?
This is an example of how to set up your data table:
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Theoretical Probability |
Count |
Experimental Probability |
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Heads |
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Tails |
Station B-Spin City
- What are the possible outcome on the spinner? What is the probability of each outcome? Label this your theoretical probability.
- Spin the spinner 50 times and record the results of each outcome. Label this data experimental probability
- Create a spinner that has the following probabilityies and draw it in your notebook: 10% yellow, 10% purple, 20% orange, 20% red, and 40% blue.
This is an example of how to set up your data table:
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Theoretical Probability |
Count |
Experimental Probability |
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Blue |
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Yellow |
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Cyan |
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Red |
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Purple |
Station C-What's in the Bag?
- Without looking, reach into the bad and choose an item. Put the item back in the bag and draw another item. Repeat 10 times nad record the outcomes.
- There are 20 items in the bag. Based on your results from 1, predict how many items of each color are present in the bag.
- Is it possible that there are colors in the bag that you did not choose during 1? Explain.
- Look in the bag and write a probability outcome for each color.
- How did your experimental probabilites compare to the theoretical probabilities?
This is an example of how to set up your data table:
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Draw Number |
Color Item |
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1 |
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2 |
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3 |
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4 |
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5 |
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6 |
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7 |
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8 |
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9 |
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10 |
Station D-Tree Diagrams
- Draw a tree diagram for the following probability experiments and then answer the questions:
- Rolling two dice. What is the probability of rolling doubles?
- Flipping a coin three times. What is a probability of flipping 3 of the same thing?
- Rolling a dice and tossing a coin. What is the probability of rolling an even number and flipping heads?
Example Tree Diagram for flipping two coins.
Process
Station A-Coin Toss
Use this link below to simulate flipping a coin. For this activity you only need to flip one coin and I have selected Penny for you. For the task directions using the link. Record the data you gather in your math journal.
Station B-Spin City
Use this link below to simulate a spinner. For the task directions using the link. Record the data you gather in your math journal. For part 3 of the task, see if you can create the spinner on the virtual spinner using the tools the simulator provides you. Set the number of sectors to 5.
http://illuminations.nctm.org/adjustablespinner/
Evaluation
| 5 | 3 | 1 | |
| Station A | All parts of the task included | Missing 1 part of the task | Missing more than 1 part of the task |
| Station B | All parts of the task included | Missing 1 part of the task | Missing more than 1 part of the task |
| Station C | All parts of the task included | Missing 1 part of the task | Missing more than 1 part of the task |
| Station D | All parts of the task included | Missing 1 part of the task | Missing more than 1 part of the task |
| Conclusion | All parts of the task included | Answers are not justified | Questions not answered |
Total Points Possible: 25
Conclusion
Answer the following questions in your math journal after you have completed all the stations. Use the informaiton from your stations to justify your answers for the first three questions. The last question should be examples you can find, be creative and really think. Do not use "flipping a coin" because that was something we did in class.
- Based on your discoveries how reliable is theoretical probability? Explain
- How closely related are the theoretical probabilities of an event and the experimental probabilities? Why?
- Is it possible to get the experimental probability closer to the theoretical probability? If so, what?
- Give three examples of how probability is used in the real world.