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Understanding Probability Models and Compound Events in Statistics

Develop probability models to find event probabilities. Compare model probabilities to observed frequencies and explain discrepancies. Understand uniform and non-uniform models. Find probabilities of compound events using lists, tables, and simulations.

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Understanding Probability Models and Compound Events in Statistics

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  1. Probability Models 7. SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7. SP.7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events 7. SP.7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

  2. Definitions • Sample Space: set of all possible outcomes in an experiment • Theoretical Probability: what you would EXPECT to happen in an experiment • Experimental probability: the results of what ACTUALLY happened in the experiment • Uniform Models: when each outcome is equally likely • Non-Uniform Models: when each outcome is NOT equally likely

  3. Uniform Models • Uniform Models: when each outcome is equally likely. • Which spinners have a uniform model?

  4. Non-Uniform Models • Non-Uniform Models: when each outcome is NOT equally likely. • Which spinners have a non-uniform model?

  5. Questions

  6. Example: • What is the sample space? • Is this a uniform model or non-uniform model? Explain.

  7. Example: • What is the sample space? • Is this a uniform model or non-uniform model? Explain.

  8. Why are the outcomes NOT equally likely

  9. Example: Using a MODEL for Experimental Probability

  10. Practice: • What is the sample space? • Is this a uniform model or non-uniform model? Explain.

  11. Practice: • What is the sample space? • Is this a uniform model or non-uniform model? Explain.

  12. Probability Models-Activity 7. SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7. SP.7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events 7. SP.7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

  13. Compound Event 7. SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7. SP.8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7. SP.8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. 7. SP.8c. Design and use a simulation to generate frequencies for compound events.

  14. Definitions • Compound Events: more than 1 event • Tree Diagram: A way to SHOW possible outcomes and sample space (like a table or chart)

  15. Example:

  16. Example: TREE DIAGRAM TABLE

  17. Tree DiagramWhat is the sample space? How many outcomes are possible?How many possibilities are there of rolling the same number on both number cubes?

  18. TableWhat is the sample space? How many outcomes are possible?How many possibilities are there of rolling two even numbers?

  19. Example 1:

  20. Example 2:

  21. More than 2 events:

  22. EXIT TICKETon your own…

  23. Compound Event- Independent Practice 7. SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7. SP.8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7. SP.8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. 7. SP.8c. Design and use a simulation to generate frequencies for compound events.

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